Exhibit 4.1

[Form of Note]

THIS SECURITY IS A GLOBAL SECURITY WITHIN THE MEANING OF THE INDENTURE HEREINAFTER REFERRED TO AND IS REGISTERED IN THE NAME OF A DEPOSITORY (AS DEFINED IN THE INDENTURE) OR A NOMINEE THEREOF. THIS GLOBAL SECURITY IS EXCHANGEABLE FOR SECURITIES REGISTERED IN THE NAME OF A PERSON OTHER THAN THE DEPOSITORY OR ITS NOMINEE ONLY IN THE LIMITED CIRCUMSTANCES DESCRIBED IN THE INDENTURE AND, UNLESS AND UNTIL IT IS EXCHANGED IN WHOLE OR IN PART FOR SECURITIES IN DEFINITIVE FORM, THIS GLOBAL SECURITY MAY NOT BE TRANSFERRED EXCEPT AS A WHOLE BY THE DEPOSITORY TO A NOMINEE OF THE DEPOSITORY, OR BY A NOMINEE OF THE DEPOSITORY TO THE DEPOSITORY OR ANOTHER NOMINEE OF THE DEPOSITORY, OR BY THE DEPOSITORY OR ANY SUCH NOMINEE TO A SUCCESSOR DEPOSITORY OR A NOMINEE OF SUCH SUCCESSOR DEPOSITORY.

UNLESS THIS SECURITY IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION (“DTC”), TO THE COMPANY (AS DEFINED BELOW) OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND ANY SECURITY ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER NAME AS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC (AND ANY PAYMENT IS MADE TO CEDE & CO. OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC) ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR OTHERWISE BY OR TO ANY PERSON IS WRONGFUL INASMUCH AS THE REGISTERED OWNER HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.

CUSIP No. 00440EAR8

ACE INA Holdings Inc.

3.35% Senior Note due 2024

ACE INA Holdings Inc., a Delaware corporation (hereinafter called the “Company”, which term includes any successor corporation under the Indenture referred to below), for value received, hereby promises to pay to Cede & Co., or registered assigns, the principal sum of                          Dollars ($                    ) on May 15, 2024 and to pay interest thereon from May 27, 2014 or from the most recent interest payment date to which interest has been paid or duly provided for, payable semi-annually on May 15 and November 15 in each year (each, an “Interest Payment Date”), commencing November 15, 2014, at the rate of 3.35% per annum, until the principal hereof (and any Additional Amounts (as defined below)) is paid or duly made available for payment. Interest on this Note shall be computed on the basis of a 360-day year of twelve 30-day months. If any Interest Payment Date or the maturity date falls on a day that is not a Business Day, the required payment shall be made on the next Business Day as if it were made on the date such payment was due and no interest shall accrue on the amount so payable

for the period from and after such Interest Payment Date or the maturity date, as the case may be, to such next Business Day. The interest so payable and punctually paid or duly provided for on any Interest Payment Date will, as provided in such Indenture, be paid to the Person in whose name this Note (or one or more Predecessor Securities) is registered at the close of business on the regular record date for such interest, which shall be May 1 or November 1 (whether or not a Business Day), as the case may be, next preceding such Interest Payment Date. Any such interest which is payable, but is not punctually paid or duly provided for, on any Interest Payment Date shall forthwith cease to be payable to the registered Holder hereof on the relevant regular record date by virtue of having been such Holder, and may be paid to the Person in whose name this Note (or one or more Predecessor Securities) is registered at the close of business on a subsequent Special Record Date (which shall be at least 10 days before the payment date) for the payment of such defaulted interest to be fixed by the Company, notice whereof shall be given to the Holders of Notes of this series not less than 10 days prior to such Special Record Date, or may be paid at any time in any other lawful manner not inconsistent with the requirements of any securities exchange on which the Notes may be listed, and upon such notice as may be required by such exchange, all as more fully provided in such Indenture. Any interest paid on this Note shall be increased to the extent necessary to pay Additional Amounts as set forth in this Note.

Payment of the principal of, interest on or any Redemption Price or Additional Amounts in respect of this Note will be made at the office or agency of the Company and the Guarantor (as defined below) maintained for that purpose in The Borough of Manhattan, The City of New York, in such coin or currency of the United States of America as at the time of payment is legal tender for payment of public and private debts; provided, however, that, at the option of the Company or the Guarantor, interest may be paid by check mailed to the address of the Person entitled thereto as such address shall appear in the Security Register; provided, further, that payment to DTC or any successor Depository may be made by wire transfer to the account designated by DTC or such successor depository in writing.

This Note is one of a duly authorized issuance of securities of the Company (herein called the “Notes”), fully and unconditionally guaranteed as to payment of principal, premium, if any, and interest by ACE Limited, a company limited by shares (Aktiengesellschaft) under the laws of Switzerland (the “Guarantor”), issued and to be issued in one or more series under an Indenture, dated as of August 1, 1999, as supplemented by the First Supplemental Indenture, dated as of March 13, 2013 (such Indenture and First Supplemental Indenture together herein called, together with all indentures supplemental thereto, the “Indenture”), among the Company, the Guarantor and The Bank of New York Mellon Trust Company, N.A. (as successor to J.P. Morgan Trust Company, National Association and The First National Bank of Chicago), as Trustee (herein called the “Trustee”, which term includes any successor trustee under the Indenture), to which the Indenture and all indentures supplemental thereto referenced is hereby made for a statement of the respective rights, limitations of rights, duties and immunities thereunder of the Company, the Guarantor, the Trustee and the Holders of the Notes, and of the terms upon which the Notes are, and are to be, authenticated and delivered. This Note is one of the series designated on the face hereof, initially limited (subject to exceptions provided in the Indenture) to the aggregate principal amount specified in the Officer’s Certificate, dated as of May 27, 2014, establishing the terms of the Notes pursuant to the Indenture.

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The Notes are senior unsecured obligations of the Company. The Company’s obligation to pay the principal of, interest on or any Additional Amounts in respect of the Notes is unconditionally guaranteed on a senior unsecured basis by the Guarantor pursuant to Article 16 of the Indenture.

If an Event of Default with respect to the Notes shall occur and be continuing, the principal of the Notes may be declared due and payable in the manner and with the effect provided in the Indenture.

The Indenture contains provisions permitting, with certain exceptions as therein provided, the amendment thereof and the modification of the rights and obligations of the Company or the Guarantor and the rights of the Holders of the Securities of each series issued under the Indenture at any time by the Company, the Guarantor and the Trustee with the written consent of the Holders of not less than a majority in aggregate principal amount of the Securities at the time Outstanding of each series affected thereby. The Indenture also contains provisions permitting the Holders of specified percentages in aggregate principal amount of the Securities of any series at the time Outstanding, on behalf of the Holders of all Securities of such series, to waive compliance by the Company or the Guarantor with certain provisions of the Indenture and certain past defaults under the Indenture and their consequences. Any such consent or waiver by the Holder of this Note shall be conclusive and binding upon such Holder and upon all future Holders of this Note and of any Notes issued upon the registration of transfer hereof or in exchange herefor or in lieu hereof, whether or not notation of such consent or waiver is made upon this Note.

This Note is not subject to any sinking fund.

No reference herein to the Indenture and no provision of this Note or of the Indenture shall alter or impair the obligation of the Company, which is absolute and unconditional, to pay the principal of, interest on or any Redemption Price or any Additional Amounts in respect of this Note, at the times, place and rate, and in the coin or currency, herein and in the Indenture prescribed.

As provided in the Indenture and subject to certain limitations set forth therein and in this Note, the transfer of this Note may be registered on the Security Register upon surrender of this Note for registration of transfer at the office or agency of the Company and the Guarantor maintained for that purpose in any place where the principal of, interest on or any Additional Amounts in respect of this Note are payable, duly endorsed by, or accompanied by a written instrument of transfer in form satisfactory to the Company and the Security Registrar duly executed by, the Holder hereof or by his attorney duly authorized in writing, and thereupon one or more new Notes of this series and of like tenor, of authorized denominations and for the same aggregate principal amount, will be issued to the designated transferee or transferees.

The Notes are issuable only in registered form without coupons in the denominations specified in the Officer’s Certificate, dated as of May 27, 2014, establishing the terms of the Notes, all as more fully provided in the Indenture and such Officer’s Certificate. As provided in the Indenture and in such Officer’s Certificate, and subject to certain limitations set forth in the Indenture, such Officer’s Certificate and in this Note, the Notes are exchangeable for a like aggregate principal amount of Notes of this series in different authorized denominations, as requested by the Holders surrendering the same.

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No service charge shall be made for any such registration of transfer or exchange, but the Company may require payment of a sum sufficient to cover any tax or other governmental charge payable in connection therewith, other than in certain cases provided in the Indenture.

Prior to due presentment of this Note for registration of transfer, the Company, the Guarantor, the Trustee and any agent of the Company, the Guarantor or the Trustee may treat the Person in whose name this Note is registered as the owner hereof for all purposes, whether or not this Note be overdue, and neither the Company, the Guarantor, the Trustee nor any such agent shall be affected by notice to the contrary.

The Notes are redeemable as a whole or in part, at the Company’s option at any time, at a Redemption Price equal to the greater of (i) 100 percent of the principal amount of the Notes to be redeemed or (ii) the sum of the present values of the remaining scheduled payments of principal and interest thereon (excluding interest accrued to the Redemption Date) and discounted to the Redemption Date on a semi-annual basis (assuming a 360-day year consisting of twelve 30-day months) at the applicable Treasury Rate plus 15 basis points, plus, in each case, accrued and unpaid interest on the principal amount being redeemed to but excluding the Redemption Date.

“Treasury Rate” means, with respect to any Redemption Date, (1) the yield, under the heading which represents the average for the immediately preceding week, appearing in the most recently published statistical release designated “H.15(519)” or any successor publication which is published weekly by the Board of Governors of the Federal Reserve System and which establishes yields on actively traded United States Treasury securities adjusted to constant maturity under the caption “Treasury Constant Maturities”, for the maturity corresponding to the Comparable Treasury Issue (if no maturity is within three months before or after the Remaining Life, yields for the two published maturities most closely corresponding to the Comparable Treasury Issue will be determined and the Treasury Rate will be interpolated or extrapolated from such yields on a straight line basis, rounding to the nearest month) or (2) if such release (or any successor release) is not published during the week preceding the calculation date or does not contain such yields, the rate per year equal to the semi-annual equivalent yield-to-maturity of the Comparable Treasury Issue, calculated using a price for the Comparable Treasury Issue (expressed as a percentage of its principal amount) equal to the Comparable Treasury Price for such Redemption Date. The Treasury Rate will be calculated on the third Business Day preceding the Redemption Date.

“Business Day” means any calendar day that is not a Saturday, Sunday or legal holiday in New York, New York, and on which commercial banks are open for business in New York, New York.

“Comparable Treasury Issue” means the United States Treasury security selected by an Independent Investment Banker as having a maturity comparable to the remaining term of the Notes to be redeemed.

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“Comparable Treasury Price” means (1) the average of four Reference Treasury Dealer Quotations for such Redemption Date, after excluding the highest and lowest Reference Treasury Dealer Quotations, or (2) if the Independent Investment Banker obtains fewer than four such Reference Treasury Dealer Quotations, the average of all such quotations.

“Independent Investment Banker” means either Goldman, Sachs & Co. or J.P. Morgan Securities LLC, or their respective successors, as may be appointed from time to time by the Company or, if neither such firm is willing or able to select the Comparable Treasury Issue, an independent investment banking institution of national standing appointed by the Company.

“Reference Treasury Dealer” means each of (1) Goldman, Sachs & Co. and J.P. Morgan Securities LLC, and their respective successors, (2) a Primary Treasury Dealer (as defined below) selected by ANZ Securities, Inc., and its successors, and (3) a Primary Treasury Dealer selected by Mitsubishi UFJ Securities (USA), Inc., and its successors; provided, however, that if any of the foregoing shall cease to be a primary U.S. Government securities dealer in New York City, which we refer to as a “Primary Treasury Dealer,” the Company will substitute another Primary Treasury Dealer.

“Reference Treasury Dealer Quotations” means, with respect to each Reference Treasury Dealer and any Redemption Date, the average, as determined by the Independent Investment Banker, of the bid and asked prices for the Comparable Treasury Issue (expressed in each case as a percentage of its principal amount) quoted in writing to the Independent Investment Banker at 5:00 p.m., New York City time, on the third Business Day preceding such Redemption Date.

All payments on this Note will be made without withholding of any present or future taxes or governmental charges of Switzerland, the Cayman Islands or Bermuda (each, a “Taxing Jurisdiction”), unless the Company is required to do so by applicable law or regulation.

If the Company is required to withhold amounts under the laws or regulations of a Taxing Jurisdiction, it will, subject to the limitations described below, pay to the Holder of this Note additional amounts so that every net payment made to the Holder of this Note, after the withholding, will be the same amount provided for in this Note and the Indenture (“Additional Amounts”).

The Company will not be required to pay any Additional Amounts for (1) any tax or governmental charge which would not have been imposed but for the fact that the Holder of this Note: (a) was a resident of, or engaged in business or maintained a permanent establishment or was physically present in, the relevant Taxing Jurisdiction or otherwise had some connection with the relevant Taxing Jurisdiction other than the mere ownership of, or receipt of payment on, this Note; (b) presented this Note for payment in the relevant Taxing Jurisdiction, unless this Note could not have been presented for payment elsewhere; or (c) presented this Note for payment more than 30 days after the date on which the payment became due unless the Holder of this Note would have been entitled to these Additional Amounts if the Holder of this Note had presented this Note for payment within the 30-day period; (2) any estate, inheritance, gift, sale, transfer, personal property or similar tax or other governmental charge; (3) any tax or other governmental charge that is imposed or withheld because of failure by the Holder of this Note to comply with any reasonable request by the Company: (a) to provide information concerning the

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nationality, residence or identity of the Holder of this Note or that of the beneficial owner of this Note; or (b) to make any claim or satisfy any information or reporting requirement, which in either case is required by the relevant Taxing Jurisdiction as a precondition to exemption from all or part of the tax or other governmental charge; (4) any tax imposed on payments on this Note under sections 1471 through 1474 of the Internal Revenue Code, any current or future regulations thereunder and official interpretations thereof, any agreements entered into pursuant to section 1471(b)(1) of the Internal Revenue Code and any fiscal or regulatory legislation, rules or official practices adopted pursuant to any published intergovernmental agreement entered into in connection with the implementation of such sections of the Internal Revenue Code (“FATCA”); or (5) any combination of items (1), (2), (3) or (4) above.

The Company will not pay Additional Amounts if the Holder of this Note is a fiduciary or partnership or other than the sole beneficial owner of this Note if the beneficiary or partner or settlor would not have been entitled to the Additional Amounts had it been the holder of this Note.

By purchasing this Note, each Holder of this Note and each beneficial owner of an interest herein agrees to provide, promptly upon request, to the Company and its agents (or other persons responsible for withholding of taxes, including by not limited to withholding of tax under FATCA or delivery of information under FATCA) information and/or properly completed and signed tax certifications sufficient to eliminate the imposition of or to determine the amount of any withholding of tax, including withholding of tax under FATCA, or to enable the Company or its agents to satisfy reporting and other obligations.

The Company will be entitled to redeem this Note, at its option, at any time as a whole but not in part, upon not less than 30 nor more than 60 days’ notice, at 100% of the principal amount thereof, plus accrued and unpaid interest (if any) to the Redemption Date (subject to the right of holders of record on the relevant record date to receive interest due on the relevant Interest Payment Date), in the event that the Company or the Guarantor has become or would become obligated to pay, on the next date on which any amount would be payable with respect to this Note, any Additional Amounts as a result of: (1) a change in or an amendment to the laws (including any regulations promulgated thereunder) of a Taxing Jurisdiction, which change or amendment is announced after May 21, 2014; or (2) any change in or amendment to any official position regarding the application or interpretation of such laws or regulations, which change or amendment is announced after May 21, 2014, and, in each case, the Company or the Guarantor, as applicable, cannot avoid such obligation by taking reasonable measures available to it.

The Indenture contains provisions whereby (i) the Company and the Guarantor may be discharged from their obligations with respect to the Notes (subject to certain exceptions) or (ii) the Company and the Guarantor may be released from their obligations under specified covenants and agreements in the Indenture, in each case if the Company or the Guarantor irrevocably deposits with the Trustee money or Government Obligations, or a combination thereof, in an amount sufficient, without consideration of any reinvestment, to pay and discharge the entire indebtedness on all Notes of this series, and satisfies certain other conditions, all as more fully provided in the Indenture.

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This Note shall be governed by and construed in accordance with the laws of the State of New York applicable to agreements and instruments made and to be performed wholly within such State.

All terms used in this Note without definition that are defined in the Indenture shall have the meanings assigned to them in the Indenture.

[Remainder of Page Intentionally Left Blank]

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Unless the Certificate of Authentication hereon has been executed by or on behalf of the Trustee under the Indenture by the manual signature of one of its authorized officers, this Note shall not be entitled to any benefits under the Indenture or be valid or obligatory for any purpose.

IN WITNESS WHEREOF, the Company has caused this instrument to be duly executed under its corporate seal.

CERTIFICATE OF AUTHENTICATION

This is one of the Securities of the series designated therein referred to in the within-mentioned Indenture.

Dated: May 27, 2014

ABBREVIATIONS

The following abbreviations, when used in the inscription on the face of this instrument, shall be construed as though they were written out in full according to applicable laws or regulations:

Additional abbreviations may also be used though not in the above list.

FOR VALUE RECEIVED, the undersigned registered holder hereby sell(s), assign(s) and transfer(s) unto

the within Note and all rights thereunder, hereby irrevocably constituting and appointing                                                                                                                                                                                         to transfer said Note on the books of the Company with full power of substitution in the premises.

Signatures must be guaranteed by an “eligible guarantor institution” meeting the requirements of the Trustee, which requirements include membership or participation in the Security Transfer Agent Medallion Program (“STAMP”) or such other “signature guarantee program” as may be determined by the Trustee in addition to, or in substitution for, STAMP, all in accordance with the Securities Exchange Act of 1934, as amended.