Exhibit 32.1

APACHE OFFSHORE INVESTMENT PARTNERSHIP

Certification of Chief Executive Officer
and Principal Financial Officer

     I, G. Steven Farris, 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, the annual report on Form 10-K of Apache Offshore Investment Partnership for the period ended December 31, 2010, fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. §78m or §78o (d)) and that information contained in such report fairly represents, in all material respects, the financial condition and results of operations of Apache Offshore Investment Partnership.

	/s/ G. Steven Farris
	By:	G. Steven Farris
	Title:	Chairman of the Board and Chief Executive Officer (principal executive officer) of Apache Corporation, Managing Partner
Date: February 28, 2011

     I, Thomas P. Chambers, 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, the annual report on Form 10-K of Apache Offshore Investment Partnership for the period ended December 31, 2010, fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. §78m or §78o (d)) and that information contained in such report fairly represents, in all material respects, the financial condition and results of operations of Apache Offshore Investment Partnership.

	/s/ Thomas P. Chambers
	By:	Thomas P. Chambers
	Title:	Executive Vice President and Chief Financial Officer (principal financial officer) of Apache Corporation, Managing Partner
Date: February 28, 2011