In worst case scenario they would overpopulate and consume all natural resources until a majority of their population starved down to an equilibrium. Eventually there would arise some predator that would adapt to take advantage of the new food supply. This would probably take thousands of not millions of years though.
Our limited human lifespans make us succeptable to thinking in short term, in the long term it wouldn’t matter in the least bit if chickens ravaged the amazon ecosystem since it would just adapt over a relatively short time geologically. 50 thousand years is unimaginable to us but peanuts to the planet and environment. Rediculously successful organisms ravaging the environment and killing themselves off is a story as old as biology.