Exhibit 99.1

Alta Mesa Holdings, LP

ALTA MESA ANNOUNCES CLOSING

OF PRIVATE OFFERING OF SENIOR NOTES

Houston, Texas – October 15, 2012 – Alta Mesa Holdings, LP (“Alta Mesa”) and its wholly-owned subsidiary, Alta Mesa Finance Services Corp., announced the closing of its private offering of $150 million in aggregate principal amount of senior notes due 2018 in a private placement to eligible investors (“Notes”). The Notes bear interest at 9.625% per annum and were issued at a price of 99% of their face amount, providing a yield to maturity of 9.850%. These Notes were offered as additional notes under an indenture pursuant to which Alta Mesa initially issued $300 million principal amount of its 9 5/8% senior notes due 2018 on October 13, 2010 (the “Existing Notes”). The Notes will be treated as a single series with, and will have the same terms as, the Existing Notes, but will not be fungible with the Existing Notes for trading purposes unless and until they are exchanged for registered notes. Alta Mesa applied the net proceeds of this private offering to repay existing indebtedness under its senior secured revolving credit facility.

The Notes were offered only to qualified institutional buyers in reliance on Rule 144A under the Securities Act, and outside the United States, only to non-U.S. investors pursuant to Regulation S. The Notes will not be registered under the Securities Act or any state securities laws and may not be offered or sold in the United States absent an effective registration statement or an applicable exemption from, or a transaction not subject to, the registration requirements of the Securities Act and applicable state securities laws. This news release does not constitute an offer to sell or a solicitation of an offer to buy any of the Notes, nor does it constitute an offer, solicitation or sale in any jurisdiction in which such offer, solicitation or sale is unlawful. This press release is being issued pursuant to and in accordance with Rule 135c under the Securities Act.

Alta Mesa Holdings, LP is a privately held company engaged primarily in onshore oil and natural gas acquisition, exploitation, exploration and production.

Forward-Looking Statements

This news release includes information that could constitute forward-looking statements made pursuant to the safe harbor provision of the Private Securities Litigation Reform Act of 1995. These statements may be identified by words such as ‘intends’, ‘will’, ‘expect’, ‘should’, ‘could’, ‘shall’ and similar expressions. These statements are subject to risks and uncertainties, and actual results and events could differ materially from what presently is expected. Factors leading thereto may include, without limitation, general economic conditions, conditions in the markets Alta Mesa is engaged in, commodity price volatility, low prices for oil and/or natural gas, global economic conditions, inflation, lack of availability of drilling and production equipment and services, environmental risks, drilling and other operating risks, regulatory changes, the uncertainty inherent in estimating oil and natural gas reserves and in projecting future rates of production, cash flow and access to capital, the timing of development expenditures, and specific risk factors discussed in other public filings made by Alta Mesa with the Securities and Exchange Commission. This list of factors is not intended to be exhaustive. Such forward-looking statements only speak as of the date of this press release, and we assume no obligation to update any written or oral forward-looking statement made by us or on our behalf as a result of new information, future events, or other factors.

FOR MORE INFORMATION CONTACT: Lance L. Weaver (281) 943-5597 lweaver@altamesa.net

15021 Katy Freeway, Suite 400 · Houston, Texas 77094 · (281) 530-0991 · www.altamesa.net