Exhibit 10.4

Execution Copy

PURCHASE AND SALE AGREEMENT

This Purchase and Sale Agreement (this “Agreement”) is entered into by and among Harry B. Rosenberg and Charles E. Dobrusin, as trustees of the trusts listed on Exhibit A attached hereto and made a part hereof (each a “Selling Trust” and collectively the “Selling Trusts”), and Hyatt Hotels Corporation, a Delaware corporation (the “Purchaser” or the “Company”), as of May 15, 2011. Each of the Selling Trusts and the Purchaser is sometimes referred to herein as a “Party” and collectively as the “Parties” to this Agreement.

Recitals

WHEREAS, the Selling Trusts own 2,000,000 shares (the “Subject Shares”) of the Class B Common Stock of the Company; and

WHEREAS, the Selling Trusts desire to sell and the Purchaser desires to purchase the Subject Shares for a price per share of $44.03, subject to the terms and provisions of this Agreement; and

WHEREAS, the number of the Subject Shares to be sold by each of the Selling Trusts is indicated on Exhibit A.

Agreement

NOW, THEREFORE, in consideration of the mutual covenants and agreements contained herein and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties hereby agree as follows:

1. Purchase and Sale. The Selling Trusts agree to sell the Subject Shares to the Purchaser, and the Purchaser agrees to purchase the Subject Shares on the Closing Date (as defined in Section 2 below), with the number of Subject Shares to be sold by each of the Selling Trusts indicated on Exhibit A. The purchase price for the Subject Shares shall be $44.03 per share, resulting in a total Purchase Price of $88,060,000 due to the Selling Trusts from the Purchaser (the “Purchase Price”), and which shall be payable in cash at the closing of such sale.

2. Closing. The closing of the transactions contemplated by this Agreement (the “Closing”) shall take place at the offices of Latham & Watkins LLP, 233 South Wacker Drive, Suite 5800, Chicago, Illinois 60606, on May 16, 2011, or on such other date as the Parties may mutually determine (the “Closing Date”).

3. Closing Deliveries of the Purchaser. At the Closing, the Purchaser shall deliver the Purchase Price to the Selling Trusts by wire transfer of immediately available funds to an account designated in writing by the Selling Trusts.

4. Closing Deliveries by Selling Trusts. At the Closing, the Selling Trusts shall deliver, or cause to be delivered, to the Purchaser, certificates representing the Subject Shares together with assignments separate from certificate with respect to the Subject Shares sufficient to transfer title to the Subject Shares to the Purchaser on the books of the Company and Certificates of Fiduciary Authority, including, as necessary, Medallion Guarantees.

5. Representations and Warranties of the Selling Trusts. Each Selling Trust, for itself and not for the other Selling Trusts, represents and warrants to the Purchaser that the statements contained in this Section 5 are true and correct as of the date of this Agreement and shall be true and correct as of the Closing Date, it being agreed that the Purchaser is relying on each statement.

(a) Power, Legal, Valid and Binding Obligations. Such Selling Trust (i) is duly organized and validly existing and (ii) has all necessary power and capacity to execute and deliver this Agreement and each of the other agreements and instruments contemplated hereby (collectively, the “Ancillary Documents”) and to perform, observe and comply with all of its agreements and obligations hereunder and thereunder and to consummate the transactions contemplated hereby and thereby. This Agreement and the Ancillary Documents to which it is or will be a party have been or will be duly and validly executed by such Selling Trust and, upon delivery thereof by each Selling Trust, will constitute the legal, valid and binding obligations of each Selling Trust, enforceable against each Selling Trust in accordance with their terms.

(b) No Conflict. None of the execution, delivery or performance by such Selling Trust of this Agreement or any Ancillary Document to which it is or will be a party will (with or without the giving of notice, the lapse of time or both) conflict with, result in a breach or violation of or constitute a default under (a) any contract, agreement or other instrument to which such Selling Trust is a party or by which it or its assets or property is bound or (b) any law, statute, rule, regulation, ordinance, writ, order or judgment to which such Selling Trust is subject or by which it or its assets or property is bound.

(c) Consents. No approval, consent, waiver or filing of or with any third party, including, but not limited to, any governmental bodies, agencies or instrumentalities, is required for the execution, delivery and performance by such Selling Trust of this Agreement or any Ancillary Document to which it is or will be a party.

(d) Title to Shares; Liens and Encumbrances. Such Selling Trust is the legal and beneficial owner of the Subject Shares listed opposite its name on attached Exhibit A and holds such Subject Shares free and clear of all liens, pledges, options, claims, encumbrances and other security arrangements or restrictions of any kind other than restrictions under that certain Amended & Restated Global Hyatt Agreement dated October 1, 2009 and under the Company’s Amended and Restated Certificate of Incorporation (collectively, “Liens”), and upon delivery of such Subject Shares to the Purchaser pursuant to the terms of this Agreement, the Purchaser will receive good and marketable title thereto, free and clear of any and all Liens.

(e) Broker’s Fees. Such Selling Trust has no liability or obligation to pay any fees or commissions to any broker, finder or agent with respect to the transactions contemplated by this Agreement for which the Purchaser could become liable or otherwise obligated.

(f) Independent Decision to Sell; Etc. Such Selling Trust has made an independent decision to sell its Subject Shares to the Purchaser and has determined that it has adequate information concerning the business and financial condition of the Company in connection with its decision to sell its Subject Shares. Such Selling Trust understands the disadvantage to which it may be subject on account of the disparity of information between it

and the Purchaser, and further acknowledges that the Company and its affiliates may possess material, non-public information not known to such Selling Trust regarding or relating to the Company, its affiliates or the Subject Shares. Such Selling Trust is capable, by reason of its business or financial knowledge and experience, of evaluating the merits and risks of the sale of its Subject Shares and of protecting its own interest in connection with the sale of the Subject Shares, and such Selling Trust acknowledges that it has had the opportunity to discuss the information available to it relating to the sale of the Subject Shares with such advisors as it has deemed appropriate. Such Selling Trust acknowledges that the Purchaser has not given it any investment advice or rendered any opinion to it as to whether the sale of the Subject Shares is prudent or suitable, and, except as expressly provided in Section 6 of this Agreement, it is not relying or any representation or warranty made by the Purchaser in connection with its decision to sell its Subject Shares to the Purchaser.

6. Representations and Warranties of the Purchaser. The Purchaser represents and warrants to each Selling Trust that the statements contained in this Section 6 are true and correct as of the date of this Agreement and shall be true and correct as of the Closing Date, it being agreed that each Selling Trust is relying on each such statement.

(a) Power, Legal, Valid and Binding Obligations. The Purchaser is a duly incorporated and validly existing corporation organized under the laws of the State of Delaware. The Purchaser has all necessary power and capacity to execute and deliver this Agreement and the Ancillary Documents, and to perform, observe and comply with all of its agreements and obligations hereunder and thereunder and to consummate the transactions contemplated hereby and thereby. This Agreement and each of the Ancillary Documents to which it is or will be a party have been or will be duly and validly executed by the Purchaser and, upon delivery thereof by the Purchaser, will constitute the legal, valid and binding obligations of the Purchaser, enforceable against it in accordance with their terms.

(b) No Conflict. None of the execution, delivery or performance by the Purchaser of this Agreement or any Ancillary Document to which it is a party will (with or without the giving of notice, the lapse of time or both) conflict with, result in a breach or violation of or constitute a default under (a) any contract, agreement or other instrument to which the Purchaser is a party or by which it or its assets or property is bound or (b) any law, statute, rule, regulation, ordinance, writ, order or judgment to which the Purchaser is subject or by which it or its assets or property is bound.

(c) Consents. No approval, consent, waiver or filing of or with any third party, including, but not limited to, any governmental bodies, agencies or instrumentalities, is required for the execution, delivery and performance by the Purchaser of this Agreement or any Ancillary Document to which it is or will be a party.

(d) Legal Matters. There is no action, suit or proceeding by or before any court or governmental or other regulatory or administrative agency or commission pending, or, to the best of the Purchaser’s knowledge, threatened against or involving the Purchaser which challenges the validity of this Agreement or any action taken or to be taken by the Purchaser pursuant to this Agreement or in connection with the transaction contemplated hereby. The Purchaser is not subject to any judgment, order or decree entered into in any lawsuit or proceeding which will have an adverse effect on the transactions contemplated hereby.

(e) Broker’s Fees. The Purchaser has no liability or obligation to pay any fees or commission to any broker, finder, or agent with respect to the transactions contemplated by this Agreement for which Selling Trusts could become liable or otherwise obligated.

(f) Non-Public Information. Purchaser acknowledges that it has not provided any information that currently constitutes material, non-public information relating to the Company to any of the Selling Trusts, and further acknowledges that no such Selling Trust has requested any such information from the Company. The Purchaser represents that its purchase of the Subject Shares is being made during an “open window” period under the Hyatt Hotels Corporation Insider Trading Compliance Program.

7. Miscellaneous.

(a) Survival of Representations and Warranties Herein. All representations, warranties and covenants set forth herein shall survive the Closing Date.

(b) Additional Documents. From time to time after execution of this Agreement, each party hereto shall, without additional consideration, execute and deliver such further agreements and instruments and take such other action as may be reasonably requested by any other party hereto in order to carry out the purposes of this Agreement.

(c) Amendment and Waiver. This Agreement cannot be amended, supplemented or modified, nor can any provision hereof be waived, except by a written instrument signed by the party against whom enforcement of such amendment, supplement, modification or waiver is sought.

(d) Notices. Any notice or other communication required or permitted to be given hereunder shall be in writing and shall be deemed to have been properly given (a) when delivered by hand; (b) when sent by facsimile or email (with acknowledgment of complete transmission); (c) three days after being sent by certified mail, return receipt requested or (d) one day after deposit with a nationally-recognized overnight delivery service, in each case to the addresses or facsimile numbers set forth on the signature page hereof. Each party hereto shall be entitled to specify a different address or facsimile number for the receipt of subsequent notices or other communications by giving written notice thereof to the other party in accordance with this Paragraph (d).

(e) Severability. If any term or provision of this Agreement, or the application thereof to any person, entity or circumstance, shall, to any extent, be determined to be contrary to law and unenforceable by any court of law, the remaining terms and provisions of this Agreement, and the application thereof to other persons, entities and circumstances, shall not be invalidated thereby, and each term and provision hereof shall be construed with all other remaining terms and provisions hereof to effect the intent of the parties to the fullest extent of the law.

(f) No Third Party Beneficiaries. This Agreement shall not confer any rights or remedies upon any person other than the parties hereto and their respective successors and permitted assigns.

(g) Governing Law. This Agreement shall be governed by and construed in accordance with the domestic laws of the State of Delaware without giving effect to any choice or conflict of law provision or rule (whether of the State of Delaware or any other jurisdiction) that would cause the application of the laws of any jurisdiction other than the State of Delaware.

(h) Entire Agreement. This Agreement, including the other writings referred to herein or delivered pursuant hereto, constitutes the entire agreement between the Parties hereto with respect to the subject matter hereof.

(i) Binding Effect. This Agreement and all the provisions hereof shall be binding upon and inure to the benefit of the Parties and their respective successors and permitted assigns.

(j) Counterparts. This Agreement may be executed in any number of separate counterparts, each of which, when so executed, shall be deemed an original, and all of said counterparts taken together shall be deemed to constitute but one and the same instrument and, any signed counterpart shall be deemed delivered by the Party signing it if sent to the other parties hereto by facsimile transmission or electronic transmission and shall be as effective as original ink signatures for the purposes of the execution and delivery of this Agreement.

(k) Confidentiality. Unless the prior written consent of the other Party is obtained, the sale and purchase of the Subject Shares and all provisions of this Agreement shall be and remain confidential to the Parties, except to the extent that such information is in the public domain or disclosure is required by law or by any regulatory body whether public or not. For the avoidance of doubt, the Parties shall be permitted to disclose the terms of this Agreement to their professional or financial advisors who aware of its confidential nature.

(l) Assignment. The Purchaser may not, without the prior written consent of the Selling Trusts, assign, grant any security interest over, hold on trust or otherwise transfer the benefit of the whole or any part of this Agreement.

(m) Costs. All costs in connection with the negotiation, preparation, execution and performance of this Agreement, and any documents referred to in it, will be borne by the Party that incurred the costs.

Signature page follows.

IN WITNESS WHEREOF, each of the Parties hereto has duly executed this Agreement as of the date first above written.

HARRY B. ROSENBERG, not individually, but solely in his capacity as co-trustee of the following Selling Trusts: JNP 2010-P.G. Trust, JNP Parachute Mirror Trust K, JNP Parachute Mirror Trust L

CHARLES E. DOBRUSIN, not individually, but solely in his capacity as co-trustee of the following Selling Trusts: JNP 2010-P.G. Trust, JNP Parachute Mirror Trust K, JNP Parachute Mirror Trust L

HYATT HOTELS CORPORATION

Exhibit A

Selling Trusts

A-1