There have been bugs, in the past, that folks have been able to exploit to get extra chicken coops, but Zynga has basically threatened folks saying that you never know what will happen to those extra coops, saying things like that it would be a shame to have 15 gold chickens in a second chicken coop suddenly vanish.
So probably best to just wait until they unlock the chicken coop expansion that they're going to make available. (No, there is no timeframe for it.)