It's not like they would actually go extinct entirely, they would just evolve in a different direction and have much smaller populations. There are wild bovines, turkeys, swines, etc. If chickens were cut loose to live in the wild, they could probably do alright for themselves, but you might see other traits favored than maximum egg-laying capacity or rapid growth that only serves to maximize farmer profit by reducing the time to be able to sell them off, for example. Local populations would likely collapse until they reached a more stable level, too, given they would have more limited food available, absent someone constantly feeding them.