Alta Mesa 10-Q 2018 Q3 Quarterly report

Exhibit 32.1

CERTIFICATION OF

CHIEF EXECUTIVE OFFICER

OF ALTA MESA HOLDINGS, LP

PURSUANT TO 18 U.S.C. SECTION 1350

In connection with this Quarterly Report on Form 10-Q of Alta Mesa Holdings, LP for the period ended June 30, 2018 I, Harlan H. Chappelle, President and Chief Executive Officer of Alta Mesa Holdings, LP, hereby certify pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

1. This Quarterly Report on Form 10-Q for the period ended September 30, 2018 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 this Quarterly Report on Form 10-Q for the period ended September 30, 2018 fairly presents, in all material respects, the financial condition and results of operations of Alta Mesa Holdings, LP for the periods presented therein.

Date: November 14, 2018

 /s/ Harlan H. Chappelle

Harlan H. Chappelle

President and Chief Executive Officer of Alta Mesa

Holdings GP, LLC, general partner of Alta Mesa Holdings, LP