Can billboard owners reject political ads?

The New York Times reports that a subsidiary of Clear Channel Communications is rejecting an anti-war ad.

"Project Billboard's representatives said the contract they signed in December with Spectacolor, a division of Clear Channel, required the antiwar group to pay $368,000 to use the billboard space from Aug. 2 through Nov. 2, Election Day. ...

A Project Billboard spokesman, Howard Wolfson, said the group planned to file a lawsuit today in federal court in Manhattan charging Clear Channel with breach of contract and asking it to live up to what the group said were the terms of the deal."

Clear Channel has a close association with the Republican Party. (See the article for details.) But the issue seems to me to be what authority Clear Channel has with respect to controlling the content of its billboards. Considering that the billboards are presumably regulated and limited in number by the city, there must be some obligation to allow free expression. But Clear Channel is not a government agency and is presumably not bound by the anti-censorship constraints under which the government operates. I don't know the answer to this. I hope an expert in the field provides some help.

The two images show two versions of the ad. When Clear Channel rejected the first version because of the bomb image, Project Billboard submitted the second, presumably acknowledging that Clear Channel had some authority over the ad content. Clear Channel seems to have rejected the second ad as well.