March 28 (Reuters) - AMC Entertainment will sell up to $250 million worth of its stock in an at-the-market offering, the theater chain said on Thursday, as it looks to bolster its cash reserves in the face of a weak box office.

Shares of the Leawood, Kansas-based company were down more than 11% in early trading, Theanex Test and have fallen about 29% so far this year.

AMC will also use the proceeds to pay down its debt and has signed a deal with firms including Citigroup Global Markets, Barclays Capital and Goldman Sachs & Co for the share sale.

Last month, the company posted a bigger-than-expected loss for the fourth quarter on higher distribution costs for Taylor Swift and Beyonce concert movies and lack of big releases from Hollywood studios after twin strikes.

As of December last year, the company has cash and cash equivalents of about $884.3 million. (Reporting by Jaspreet Singh in Bengaluru; Editing by Shailesh Kuber)