Exhibit 32(1)

CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Hess Corporation (the “Corporation”) on Form 10-Q for the period ending September 30, 2008 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, John B. Hess, Chairman of the Board and Chief Executive Officer of the Corporation, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1)	The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and
(2)	The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Corporation.

By	/s/ John B. Hess
	JOHN B. HESS
	CHAIRMAN OF THE BOARD AND CHIEF EXECUTIVE OFFICER Date: November 6, 2008

A signed original of this written statement required by Section 906 has been provided to Hess Corporation and will be retained by Hess Corporation and furnished to the Securities and Exchange Commission or its staff upon request.

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