UNITED STATES
SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a) of the
Securities Exchange Act of 1934 (Amendment No. )

Filed by the Registrant þ

Filed by a Party other than the Registrant o

     Check the appropriate box:

	o		Preliminary Proxy Statement
	o		Confidential, for Use of the Commission Only (as permitted by Rule 14a-6(e)(2))
	o		Definitive Proxy Statement
	þ		Definitive Additional Materials
	o		Soliciting Material Pursuant to Section 240.14a-12

HESS CORPORATION

(Name of Registrant as Specified In Its Charter)
(Name of Person(s) Filing Proxy Statement, if other than the Registrant)

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YOUR VOTE IS IMPORTANT
PLEASE VOTE YOUR PROXY TODAY

April 21, 2010

Dear Stockholder:

     According to our latest records, we have not received your voting instructions for the important annual meeting of Hess Corporation to be held on Wednesday, May 5, 2010. Your vote is extremely important, no matter how many shares you hold.

     In the past, your broker may have voted uninstructed shares on your behalf on routine proposals such as the Election of Directors. However, due to recent NYSE and SEC rule changes, the Election of Directors is now considered a non-routine proposal and brokers will no longer be able to vote your uninstructed shares on this proposal. If you do not vote your shares in the Election of Directors, they will remain unvoted.

     You should read carefully and consider the information contained in the proxy statement, dated March 25, 2010, which you have previously received or which may be viewed over the Internet by following the instructions on the enclosed Notice of Internet Availability of Proxy Materials. For the reasons set forth in the proxy statement, the Board of Directors unanimously recommends that you vote “FOR” all directors in Proposal 1, “FOR” Proposals 2 and 3 and “AGAINST” Proposal 4. Please sign, date and return the enclosed voting instruction form as soon as possible or, alternatively, vote via the Internet or telephone as instructed on the enclosed Notice.

     On behalf of your Board of Directors, thank you for your cooperation and continued support.

Sincerely,

George C. Barry
Corporate Secretary

YOUR VOTE IS IMPORTANT
PLEASE VOTE YOUR PROXY TODAY

April 21, 2010

Dear Stockholder:

     According to our latest records, we have not received your voting instructions for the important annual meeting of Hess Corporation to be held on Wednesday, May 5, 2010. Your vote is extremely important, no matter how many shares you hold.

     You should read carefully and consider the information contained in the proxy statement, dated March 25, 2010, which you have received or which may be viewed over the Internet by following the instructions on the enclosed Notice of Internet Availability of Proxy Materials. For the reasons set forth in the proxy statement, the Board of Directors unanimously recommends that you vote “FOR” all directors in Proposal 1, “FOR” Proposals 2 and 3 and “AGAINST” Proposal 4. Please sign, date and return your proxy card as soon as possible or, alternatively, you can vote via the Internet or telephone as instructed on the enclosed notice.

     On behalf of your Board of Directors, thank you for your cooperation and continued support.

Sincerely,

George C. Barry
Corporate Secretary