Exhibit 10.1

SHARE REPURCHASE AGREEMENT

THIS SHARE REPURCHASE AGREEMENT (this “Agreement”) is made and entered into as of this 14th day of May, 2014, by and between Hercules Holding II, LLC (the “Seller”) and HCA Holdings, Inc., a Delaware corporation (the “Purchaser”).

RECITALS

WHEREAS, on May 14, 2014, a demand registration notice was delivered to the Purchaser regarding the offer and sale of shares of Common Stock, par value $0.01 per share, of the Purchaser (the “Common Stock”), to the public in a registered underwritten public offering, on the terms and conditions set forth in such demand registration notice (the “Secondary Offering”).

WHEREAS, concurrently with and subject to completion of the Secondary Offering, the Seller desires to sell to the Purchaser, and the Purchaser desires to purchase from the Seller, a number of shares of Common Stock having an aggregate value of $750,000,000, at a price equal to the price at which the underwriters have agreed to purchase the shares in the Secondary Offering, on the terms and conditions set forth in this Agreement (the “Repurchase Transaction”).

WHEREAS, after due consideration, the Audit and Compliance Committee of the Board of Directors of the Purchaser and the Board of Directors of the Purchaser have approved the Repurchase Transaction and related transactions that may be required in connection with the Repurchase Transaction.

NOW, THEREFORE, in consideration of the premises and the agreements set forth below, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties agree as follows:

ARTICLE I

SALE AND PURCHASE OF COMMON SHARES

Section 1.1 Purchase. Subject to the terms and conditions of this Agreement, at the Closing (as defined below), the Seller shall sell, assign, transfer, convey and deliver to the Purchaser, and the Purchaser shall purchase, acquire and accept from the Seller, the number of shares of Common Stock (the “Shares”) equal to $750,000,000.00 divided by the Purchase Price (as defined below), rounded down to the nearest whole share. The purchase price for each Share shall be equal to the price at which the underwriters have agreed to purchase the shares in the Secondary Offering (the “Purchase Price”).

Section 1.2 Closing. The closing of the Repurchase Transaction (the “Closing”) will take place concurrently with the closing of the Secondary Offering and the delivery to the underwriters of the shares purchased in the Secondary Offering (the “Closing Date”). At the Closing, (a) the Seller shall deliver or cause to be delivered to the Purchaser all of the Seller’s right, title and interest in and to the Shares by an appropriate method reasonably agreed to by the Purchaser and the Seller, together, in each case, with all documentation reasonably necessary to transfer to Purchaser right, title and interest in and to the Shares and (b) the Purchaser shall pay to the Seller the Purchase Price in cash by wire transfer of immediately available funds in accordance with the wire transfer instructions provided by the Seller to the Purchaser.

ARTICLE II

REPRESENTATIONS AND WARRANTIES OF THE SELLER

The Seller hereby makes the following representations and warranties to the Purchaser, each of which is true and correct on the date hereof and the Closing Date and shall survive the Closing Date.

Section 2.1 Existence and Power.

(a) Seller has the power, authority and capacity to execute and deliver this Agreement, to perform its obligations hereunder, and to consummate the transactions contemplated hereby.

(b) The execution and delivery of this Agreement by Seller and the consummation by the Seller of the transactions contemplated hereby (i) do not require the consent, approval, authorization, order, registration or qualification of, or (except for filings pursuant to Section 16 or Regulation 13D under the Securities Exchange Act of 1934) filing with, any governmental authority or court, or body or arbitrator having jurisdiction over the Seller; and (ii) except as would not have an adverse effect on the ability of Seller to consummate the transactions contemplated by this Agreement, do not and will not constitute or result in a breach, violation or default under any note, bond, mortgage, deed, indenture, lien, instrument, contract, agreement, lease or license, whether written or oral, express or implied, to which the Seller is a party or with the Seller’s organizational documents, or any statute, law, ordinance, decree, order, injunction, rule, directive, judgment or regulation of any court, administrative or regulatory body, governmental authority, arbitrator, mediator or similar body on the part of Seller or cause the acceleration or termination of any obligation or right of the Seller or any other party thereto.

Section 2.2 Valid and Enforceable Agreement; Authorization. This Agreement has been duly executed and delivered by Seller and constitutes a legal, valid and binding obligation of Seller, enforceable against the Seller in accordance with its terms, except as limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance and other similar laws of general application affecting enforcement of creditors’ rights generally and general principles of equity.

Section 2.3 Title to Shares. Seller has good and valid title to the Shares beneficially owned by it free and clear of any lien, encumbrance, pledge, charge, security interest, mortgage, title retention agreement, option, equity or other adverse claim, and has not, in whole or in part, (a) assigned, transferred, hypothecated, pledged or otherwise disposed of the Shares or its ownership rights in such Shares, or (b) given any person or entity any transfer order, power of attorney or other authority of any nature whatsoever with respect to such Shares.

Section 2.4 Sophistication of Seller. Seller acknowledges and agrees that, except as set forth in this Agreement, the Purchaser is not making any express or implied warranties in connection with the Repurchase Transaction. Seller has such knowledge and experience in financial and business matters and in making investment decisions of this type that it is capable of evaluating the merits and risks of making their investment decision regarding the Repurchase Transaction and of making an informed investment decision. Seller and/or Seller’s advisor(s) have had a reasonable opportunity to ask questions of and receive answers from a person or persons acting on behalf of the Purchaser concerning the Shares and the Purchaser and all such questions have been answered to the Seller’s full satisfaction. Seller is not relying on the Purchaser with respect to the tax and other economic considerations of the Repurchase Transaction, and Seller has relied on the advice of, or have consulted with, Seller’s own advisors.

ARTICLE III

REPRESENTATIONS AND WARRANTIES OF THE PURCHASER

The Purchaser hereby makes the following representations and warranties to the Seller, each of which is true and correct on the date hereof and the Closing Date and shall survive the Closing Date.

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Section 3.1 Existence and Power.

(a) The Purchaser is a corporation duly organized, validly existing and in good standing under the laws of the State of Delaware and has the power, authority and capacity to execute and deliver this Agreement, to perform the Purchaser’s obligations hereunder, and to consummate the transactions contemplated hereby.

(b) The execution and delivery of this Agreement by the Purchaser and the consummation by the Purchaser of the transactions contemplated hereby (i) does not require the consent, approval, authorization, order, registration or qualification of, or filing with, any governmental authority or court, or body or arbitrator having jurisdiction over the Purchaser; and (ii) except as would not have an adverse effect on the ability of Purchaser to consummate the transactions contemplated by this Agreement, does not and will not constitute or result in a breach, violation or default under, any note, bond, mortgage, deed, indenture, lien, instrument, contract, agreement, lease or license, whether written or oral, express or implied, to which Purchaser is a party, with the Purchaser’s articles of incorporation or code of regulations, or any statute, law, ordinance, decree, order, injunction, rule, directive, judgment or regulation of any court, administrative or regulatory body, governmental authority, arbitrator, mediator or similar body on the part of the Purchaser or cause the acceleration or termination of any obligation or right of the Purchaser or any other party thereto.

Section 3.2 Valid and Enforceable Agreement; Authorization. This Agreement has been duly executed and delivered by the Purchaser and constitutes a legal, valid and binding obligation of the Purchaser, enforceable against the Purchaser in accordance with its terms, except as limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance and other similar laws of general application affecting enforcement of creditors’ rights generally and general principles of equity.

Section 3.3 Sufficient Funds. Purchaser has as of the date hereof and will have as of the Closing Date access to fully committed funds sufficient to consummate the transactions contemplated by this Agreement.

ARTICLE IV

MISCELLANEOUS PROVISIONS

Section 4.1 Notice. Any notice provided for in this Agreement shall be in writing and shall be either personally delivered, or mailed first class mail (postage prepaid) with return receipt requested or sent by reputable overnight courier service (charges prepaid) to the address and to the attention of the person set forth in this Agreement. Notices will be deemed to have been given hereunder when delivered personally, three business days after deposit in the U.S. mail postage prepaid with return receipt requested and two business days after deposit postage prepaid with a reputable overnight courier service for delivery on the next business day.

If delivered to the Purchaser, to:

HCA Holdings, Inc.

One Park Plaza

Nashville, TN 37203

Attention: General Counsel

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with a copy to:

Simpson Thacher & Bartlett LLP

425 Lexington Avenue

New York, NY 10017

Attention: Joseph Kaufman

if to the Seller, to:

Hercules Holding II, LLC

c/o Kohlberg Kravis Roberts & Co. L.P.

9 West 57th Street

New York, NY 10019

Attention: Terence P. Gallagher

Facsimile No.: (212) 230-9449

Section 4.2 Entire Agreement. This Agreement and the other documents and agreements executed in connection with the Repurchase Transaction embody the entire agreement and understanding of the parties hereto with respect to the subject matter hereof and supersede all prior and contemporaneous oral or written agreements, representations, warranties, contracts, correspondence, conversations, memoranda and understandings between or among the parties or any of their agents, representatives or affiliates relative to such subject matter, including, without limitation, any term sheets, emails or draft documents.

Section 4.3 Assignment; Binding Agreement. This Agreement and the various rights and obligations arising hereunder shall inure to the benefit of and be binding upon the parties hereto and their successors and assigns.

Section 4.4 Counterparts. This Agreement may be executed in multiple counterparts, and on separate counterparts, each of which shall be deemed an original, but all of which taken together shall constitute one and the same instrument. Any counterpart or other signature hereupon delivered by facsimile shall be deemed for all purposes as constituting good and valid execution and delivery of this Agreement by such party.

Section 4.5 Governing Law. This Agreement shall in all respects be construed in accordance with and governed by the substantive laws of the State of Delaware, without giving effect to principles of conflicts of laws. Each party hereto waives, to the fullest extent permitted by applicable law, any right it may have to a trial by jury in respect of any action, suit or proceeding arising out of or relating to this Agreement or any transaction contemplated hereby.

Section 4.6 No Third Party Beneficiaries or Other Rights. Nothing herein shall grant to or create in any person not a party hereto, or any such person’s dependents or heirs, any right to any benefits hereunder, and no such party shall be entitled to sue any party to this Agreement with respect thereto.

Section 4.7 Release. Except in respect of any claim of a breach of this Agreement, (i) the Seller does hereby release the Purchaser, its shareholders, its affiliates and successors, and all of the Purchaser’s directors, officers, employees and agents (collectively, the “Company Parties”), and agree to hold them, and each of them, harmless from any and all claims or causes of action that the Seller may now have or know about, or hereafter may learn about, arising out of or in any way connected with the Repurchase Transaction and the Seller agrees that the Seller will not file any claim, charge, or lawsuit for the purpose of obtaining any monetary awards in connection with the Repurchase Transaction, and (ii) Purchaser does hereby release Seller, its general and limited partners, affiliates and successors, and all of the Seller’s directors, officers, managers, members, employees and agents (collectively, the “Seller

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Parties”), and agree to hold them, and each of them, harmless from any and all claims or causes of action that Purchaser may now have or know about, or hereafter may learn about, arising out of or in any way connected with the Repurchase Transaction and Purchaser agrees that Purchaser will not file any claim, charge, or lawsuit for the purpose of obtaining any monetary awards in connection with the Repurchase Transaction. The parties acknowledge that the foregoing release includes, but is not limited to, any claim arising under any federal, state, or local law, whether statutory or judicial, or ordinance, or any administrative regulation.

Section 4.8 Waiver; Consent. This Agreement and its terms may not be changed, amended, waived, terminated, augmented, rescinded or discharged (other than in accordance with its terms), in whole or in part, except by a writing executed by the parties hereto.

Section 4.9 No Broker. Except as previously disclosed to each other party, no party has engaged any third party as broker or finder or incurred or become obligated to pay any broker’s commission or finder’s fee in connection with the transactions contemplated by this Agreement.

Section 4.10 Further Assurances. Each party hereto hereby agrees to execute and deliver, or cause to be executed and delivered, such other documents, instruments and agreements, and take such other actions consistent with the terms of this Agreement as may be reasonably necessary in order to accomplish the transactions contemplated by this Agreement.

Section 4.11 Costs and Expenses. Each party hereto shall each pay their own respective costs and expenses, including, without limitation, any commission or finder’s fee to any broker or finder, incurred in connection with the negotiation, preparation, execution and performance of this Agreement.

Section 4.12 Severability. If any one or more of the provisions contained herein, or the application thereof in any circumstance, is held invalid, illegal or unenforceable, the validity, legality and enforceability of any such provision in every other respect and of the remaining provisions contained herein shall not be affected or impaired thereby.

Section 4.13 Termination. This Agreement may be terminated and the Repurchase Transaction abandoned at any time prior to the Closing Date (a) by mutual written consent of each party or (b) by either party if the Secondary Offering has not been completed by June 13, 2014.

(Signatures appear on the next page.)

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IN WITNESS WHEREOF, each of the parties hereto has caused this Agreement to be executed as of the date first above written.

[Signature Page to Share Repurchase Agreement]

[Signature Page to Share Repurchase Agreement]