Exhibit 99.1

CARMIKE CINEMAS ANNOUNCES INTENTION TO ADJOURN SPECIAL MEETING UNTIL JULY 25, 2016

COLUMBUS, Georgia, July 14, 2016 – Carmike Cinemas, Inc. (NASDAQ: CKEC) (“Carmike”) today announced that in light of ongoing discussions between Carmike and AMC Entertainment Holdings, Inc. (NYSE:AMC) (“AMC”) regarding the previously announced merger agreement between AMC and Carmike, Carmike intends to adjourn the Special Meeting of Stockholders scheduled for July 15, 2016.

Carmike intends to reconvene the Special Meeting on July 25, 2016 at 9:00 a.m. local time, at the offices of King & Spalding LLP located at 1180 Peachtree Street, N.E., Atlanta, Georgia 30309. The record date for stockholders entitled to vote at the Special Meeting remains May 18, 2016.

There can be no assurances regarding the outcome of any discussions between Carmike and AMC regarding the previously announced merger agreement.

Carmike stockholders who have questions or need assistance voting their shares can contact Innisfree M&A Incorporated, the firm assisting Carmike in its solicitation of proxies in connection with the AMC transaction, at (888) 750-5834 (toll-free).

About Carmike Cinemas (www.carmike.com)

Carmike Cinemas, Inc. is a U.S. leader in digital cinema, 3-D cinema deployments and alternative programming and is one of the nation’s largest motion picture exhibitors. Carmike has 273 theatres with 2,938 screens in 41 states. The circuit includes 55 premium large format (PLF) auditoriums featuring state-of-the-art technology and luxurious seating, including 32 “BigDs,” 21 IMAX auditoriums and two MuviXL screens. As “America’s Hometown Theatre Chain” Carmike’s primary focus is mid-sized communities. Visit www.carmike.com for more information.

Disclosure Regarding Forward-Looking Statements

This press release contains forward-looking statements within the meaning of the federal securities laws. Statements that are not historical facts, including statements about Carmike’s beliefs, expectations and future performance, are forward-looking statements. Forward-looking statements include statements preceded by, followed by or that include the words, “believes,” “expects,” “anticipates,” “plans,” “estimates,” “seeks” or similar expressions. Forward-looking statements are only predictions and are not guarantees of performance. These statements are based on beliefs and assumptions of Carmike’s management, which in turn are based on currently available information. The forward-looking statements also involve risks and uncertainties, which could cause actual results to differ materially from those contained in any forward-looking statement. Many of these factors are beyond Carmike’s ability to control or predict. Important factors that could cause actual results to differ materially from those contained in any forward-looking statement include, but are not limited to: the occurrence of any event, change or other circumstances that could give rise to the termination of the merger agreement with AMC; the inability to complete the proposed merger due to the failure to obtain Carmike stockholder or regulatory approval for the proposed merger or the failure to satisfy other conditions of the proposed merger within the proposed timeframe or at all; disruption in key business activities or any impact on Carmike’s relationships with third parties as a result of the announcement of the proposed merger; the failure to obtain the necessary financing arrangements as set forth in the debt commitment letters delivered pursuant to the merger agreement with AMC, or the failure of the proposed merger to close for any other reason; risks related to disruption of management’s attention from Carmike’s ongoing business operations due to the proposed

merger; the outcome of any legal proceedings, regulatory proceedings or enforcement matters that may be instituted against Carmike and others relating to the merger agreement with AMC; the risk that the pendency of the proposed merger disrupts current plans and operations and the potential difficulties in employee retention as a result of the pendency of the proposed merger; the amount of the costs, fees, expenses and charges related to the proposed merger; adverse regulatory decisions; unanticipated changes in the markets for Carmike’s business segments; general economic conditions in Carmike’s regional and national markets; Carmike’s ability to comply with covenants contained in the agreements governing Carmike’s indebtedness; Carmike’s ability to operate at expected levels of cash flow; financial market conditions including, but not limited to, changes in interest rates and the availability and cost of capital; Carmike’s ability to meet its contractual obligations, including all outstanding financing commitments; the availability of suitable motion pictures for exhibition in Carmike’s markets; competition in Carmike’s markets; competition with other forms of entertainment; the effect of Carmike’s leverage on its financial condition; prices and availability of operating supplies; the impact of continued cost control procedures on operating results; the impact of asset impairments; the impact of terrorist acts; changes in tax laws, regulations and rates; and financial, legal, tax, regulatory, legislative or accounting changes or actions that may affect the overall performance of Carmike’s business.

Consider these factors carefully in evaluating the forward-looking statements. Additional factors that may cause results to differ materially from those described in the forward-looking statements are set forth in Carmike’s Annual Report on Form 10-K for the fiscal year ended December 31, 2015, which was filed with the SEC on February 29, 2016, under the heading “Item 1A. Risk Factors,” and in its subsequently filed reports with the U.S. Securities and Exchange Commission (the “SEC”), including Forms 10-Q and 8-K. Readers are cautioned not to place undue reliance on the forward-looking statements included in this presentation, which speak only as of the date hereof. Carmike does not undertake to update any of these statements in light of new information or future events, except as required by applicable law.

Important Additional Information Regarding the Merger

This press release may be deemed to be solicitation material in respect of the proposed merger of Carmike with and into a wholly-owned subsidiary of AMC. In connection with the proposed merger, Carmike filed a definitive proxy statement with the SEC on May 23, 2016. Carmike mailed the definitive proxy statement to its stockholders on or about May 25, 2016. BEFORE MAKING ANY VOTING DECISION, CARMIKE’S STOCKHOLDERS ARE URGED TO READ THE DEFINITIVE PROXY STATEMENT IN ITS ENTIRETY AND ANY OTHER DOCUMENTS TO BE FILED WITH THE SEC IN CONNECTION WITH THE PROPOSED MERGER OR INCORPORATED BY REFERENCE IN THE DEFINITIVE PROXY STATEMENT BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION ABOUT THE PROPOSED MERGER.

Carmike’s stockholders are able to obtain a free copy of the definitive proxy statement and other relevant documents filed by Carmike with the SEC at the SEC’s website at www.sec.gov. In addition, Carmike’s stockholders may obtain a free copy of the proxy statement and other relevant documents from Carmike’s website at http://www.carmikeinvestors.com/.

Participation in the Solicitation

Carmike and its directors, executive officers and certain other members of management and employees of Carmike may be deemed to be “participants” in the solicitation of proxies from Carmike’s stockholders in connection with the proposed merger. Information regarding the interests of the persons who may, under the rules of the SEC, be considered participants in the solicitation of Carmike’s stockholders in connection with the proposed merger, which may be different than those of Carmike’s stockholders generally, is set forth in the definitive proxy statement filed with the SEC on May 23, 2016. Carmike’s stockholders may obtain a free copy of the definitive proxy statement from Carmike in the manner set forth above.

Carmike Contacts

Investor Relations:

Richard B. Hare, 706-576-3416

Chief Financial Officer

or

Innisfree M&A

Arthur Crozier or Larry Miller

212-750-5833

info@innisfreema.com

Media Contacts:

Joele Frank, Wilkinson Brimmer Katcher

Barrett Golden or Mahmoud Siddig

212-355-4449