UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a) of the Securities

Exchange Act of 1934

Filed by the Registrant  x                             Filed by a Party other than the Registrant  ¨

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¨ Preliminary Proxy Statement

¨ Confidential, for Use of the Commission Only (as permitted by Rule 14a-6(e)(2))

¨ Definitive Proxy Statement

¨ Definitive Additional Materials

x Soliciting Material under Rule 14a-12

Carmike Cinemas, Inc.

(Name of Registrant as Specified In Its Charter)

(Name of Person(s) Filing Proxy Statement, if other than the Registrant)

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EXPLANATORY NOTE

On June 14, 2016, Carmike Cinemas, Inc. mailed the attached letter to its stockholders.

June 14, 2016

Dear Stockholder,

We have previously sent to you proxy materials for the Special Meeting of Stockholders of Carmike Cinemas, Inc. to be held on June 30, 2016, to vote on the adoption of the merger agreement with AMC Entertainment Holdings, Inc. Your Board of Directors unanimously recommends that stockholders vote FOR all of the proposals on the agenda.

Your vote is important, no matter how many or how few shares you own. Please take the time to vote your shares TODAY—by telephone, via the Internet, or by signing, dating and returning the enclosed proxy card in the postage-paid envelope provided.

Sincerely,

S. David Passman III

President and Chief Executive Officer

YOUR VOTE IS IMPORTANT!

Remember, you can vote your shares by telephone or via the Internet.

Please follow the easy instructions on the enclosed proxy card.

If you have any questions, or need assistance in voting

your shares, please call our proxy solicitor,

INNISFREE M&A INCORPORATED

TOLL-FREE, at 1-888-750-5834.

Important Additional Information Regarding the Merger

This document may be deemed to be solicitation material in respect of the proposed merger of Carmike Cinemas, Inc. (the “Company”) with and into a wholly-owned subsidiary of AMC Entertainment Holdings, Inc. In connection with the proposed merger, the Company filed a definitive proxy statement with the U.S. Securities and Exchange Commission (the “SEC”) on May 23, 2016. The Company mailed the definitive proxy statement to its stockholders on or about May 25, 2016. BEFORE MAKING ANY VOTING DECISION, THE COMPANY’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.

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

Participation in the Solicitation

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