Exhibit 99.4

July 1, 2015

Dear Management Team,

This morning we issued a press release announcing that Chubb has agreed to be acquired by ACE Limited for $28.3 billion. Each Chubb shareholder will receive approximately $124.13 per Chubb share owned, about half in cash and half in ACE stock. We also posted a Corporate Note for all employees.

This transaction will elevate the two companies into an elite group of global P&C insurers – with significant financial strength, a stronger global presence, a wider range of product offerings and greater resources to invest in the business. Importantly, the combined company will adopt the Chubb name – a clear indication of ACE’s respect for the Chubb brand and the attributes and heritage of quality and outstanding service it represents.

We recognize that in any transaction of this nature, there are bound to be questions from colleagues who are concerned about how this transaction may impact them specifically. Because the transaction has just been announced and the integration process will take some time, many decisions regarding the combined company have not yet been made. Rest assured we are committed to maintaining regular communication with all employees as the transaction closes and the integration process plays out and to ensuring that any employees that are impacted by the transaction are treated fairly.

We encourage you to organize face-to-face meetings with members of your team over the next day or so to discuss the transaction and the underlying rationale. If you are asked questions that you are not yet equipped to answer, please do not speculate. Simply reply that you are not in a position to respond at this time but will pass on additional information as it becomes available.

The transaction is expected to close in the first quarter of 2016. Until then it is business as usual at Chubb, and it is important that we continue delivering the same level of service to our producers and policyholders for which Chubb is renowned.

I remain grateful for your continued support.

Sincerely,

John Finnegan

CAUTIONARY STATEMENT REGARDING FORWARD-LOOKING INFORMATION

Certain statements contained in this communication may be deemed to be forward-looking statements under certain securities laws, including the “safe harbor” provisions of the United States Private Securities Litigation Reform Act of 1995. These forward-looking statements include, but are not limited to, statements about the expected effects of the acquisition of Chubb by ACE, the expected timing of the acquisition and other statements other than in relation to historical facts. Forward-looking statements are typically identified by words such as “believe”, “expect”, “foresee”, “forecast”, “anticipate”, “intend”, “estimate”, “goal”, “plan” and “project” and similar expressions of future or conditional verbs such as “will”, “may”, “should”, “could”, or “would”.

By their very nature, forward-looking statements require us to make assumptions and are subject to inherent risks and uncertainties, many of which are outside the control of ACE and Chubb. Forward-looking statements speak only as of the date they are made and, except as required by law, neither party assumes an obligation to update the forward-looking statements contained in this communication. Any annualized, pro forma, projected and estimated numbers in this communication are used for illustrative purposes only, are not forecasts and may not reflect actual results. We caution readers not to place undue reliance on these statements as a number of important factors could cause our actual results to differ materially from the expectations expressed in such forward-looking statements. These factors include, but are not limited to, the possibility that the proposed transaction does not close when expected or at all because required regulatory, shareholder or other approvals are not received or other conditions to the closing are not satisfied on a timely basis or at all, or that the anticipated benefits of the transaction are not realized when expected or at all, including as a result of the strength of the economy and competitive factors in the areas where ACE and Chubb do business; the impact of changes in the laws and regulations regulating insurance services and enforcement thereof; the effects of competition in the markets in which ACE and Chubb operate; judicial or regulatory judgments and legal proceedings; ACE’s ability to complete the acquisition and integration of Chubb successfully; and other factors that may affect future results of ACE and Chubb.

We caution that the foregoing list of important factors is not exhaustive. Additional information about these and other factors can be found in ACE’s 2014 Annual Report on Form 10-K and Chubb’s 2014 Annual Report on Form 10-K, each filed with the U.S. Securities and Exchange Commission (the “SEC”) and available at the SEC’s website (http://www.sec.gov).

IMPORTANT ADDITIONAL INFORMATION

In connection with the proposed transaction, ACE will file with the SEC a Registration Statement on Form S-4 that will include a Joint Proxy Statement of ACE and Chubb, and a Prospectus of ACE, as well as other relevant documents concerning the proposed transaction. The proposed transaction involving ACE and Chubb will be submitted to ACE and Chubb shareholders for their consideration. This communication does not constitute an offer to sell or the solicitation of an offer to buy any securities or a solicitation of any vote or approval. SHAREHOLDERS OF ACE AND CHUBB ARE URGED TO READ THE REGISTRATION STATEMENT AND THE JOINT PROXY STATEMENT/PROSPECTUS REGARDING THE TRANSACTION WHEN IT BECOMES AVAILABLE AND ANY OTHER RELEVANT DOCUMENTS FILED WITH THE SEC, AS WELL AS ANY AMENDMENTS OR SUPPLEMENTS TO THOSE DOCUMENTS, BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION. Shareholders will be able to obtain a free copy of the definitive joint proxy statement/prospectus, as well as other filings containing information about ACE and Chubb, without charge, at the SEC’s website (http://www.sec.gov). Copies of the joint proxy statement/prospectus and the filings with the SEC that will be incorporated by reference in the joint proxy statement/prospectus can also be obtained, without charge, by directing a request to ACE Limited, 17 Woodbourne Avenue, Hamilton, HM08, Bermuda, Attention: Investor Relations, 441-299-9283, or to The Chubb Corporation, 15 Mountain View Road, P.O. Box 1615, Warren, New Jersey 07061, Attention: Investor Relations, 908-903-2365.

PARTICIPANTS IN THE SOLICITATION

ACE, Chubb, their respective directors and executive officers and other persons may be deemed to be participants in the solicitation of proxies in respect of the proposed transaction. Information regarding ACE’s directors and executive officers is available in ACE’s proxy statement for its 2015 Annual General Meeting of Shareholders filed with the SEC on April 8, 2015. Information regarding Chubb’s directors and executive officers is available in Chubb’s proxy statement for its 2015 Annual Meeting of Shareholders filed with the SEC on March 13, 2015. Other information regarding the participants in the proxy solicitation and a description of their direct and indirect interests, by security holdings or otherwise, will be contained in the joint proxy statement/prospectus and other relevant materials filed with the SEC. Free copies of this document may be obtained as described in the preceding paragraph.