Exhibit 32.2

CERTIFICATION PURSUANT TO SECTION 906

OF THE SARBANES-OXLEY ACT OF 2002 (18 U.S.C. SECTION 1350)

In connection with the Quarterly Report of Chevron Corporation (the “Company”) on Form 10-Q for the period ended September 30, 2011, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Patricia E. Yarrington, Vice President and Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to my knowledge:

(1)  the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)  the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/S/    PATRICIA E. YARRINGTON

Patricia E. Yarrington

Vice President and

Chief Financial Officer

Dated: November 3, 2011

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