EXHIBIT 32.1

CERTIFICATION OF

CHIEF EXECUTIVE OFFICER

PURSUANT TO 18 U.S.C. SECTION 1350

I, James T. Hackett, Interim Chief Executive Officer of Alta Mesa Holdings, GP, LLC, the general partner of Alta Mesa Holdings, LP (the “Company”), certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that, to the best of my knowledge:

1. The Quarterly Report on Form 10-Q of the Company for the period ended June 30, 2019 (the “Report”) fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934 (15 U.S.C. 78m); and

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

Date: August 27, 2019

/s/ James T. Hackett

James T. Hackett

Interim Chief Executive Officer

Alta Mesa Holdings GP, LLC

(as general partner of Alta Mesa Holdings, LP)

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