Hess (HES) 10-K 2005 FY Annual report

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 Annual Report of Amerada Hess Corporation (the Corporation) on Form 10-K for the period ending December 31, 2005 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: March 9, 2006