Chipotle Mexican Grill Inc. is reportedly near a deal with one of its biggest investors regarding its board of directors.

The Wall Street Journal reported that the Denver restaurant chain (NYSE: CMG) is nearing a possible settlement with billionaire investor William Ackman and his Pershing Square Capital Management investment firm regarding a possible Pershing Square seat on the board.

Ackman bought more than $1 billion worth of Chipotle shares in September, and now is its second-largest investor, owning nearly 10 percent of the company. Last month, Chipotle hired high-profile investment bankers, lawyers and public relations professionals in an attempt to defend potential actions planned by Ackman.

Chipotle's been under fire for its current board, with some activist investors this month calling for CEO Steve Ells' removal as board chairman, because "an independent board chair is an essential part of curing the company’s governance and strategic failures that have become more apparent since last year’s foodborne illness crisis."

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