One answer to eliminating rats near your chickens is to simply get a feeder that will keep the rats out and then the rats will soon go somewhere else to find food.
I got a "rat-free" chicken feeder from "thecarpentershop.net" and it uses a treadle bar where the chickens step on and the door will swing open, then when they finish and leave the treadle the door will swing shut and rats can't get to the food. You will see the rats disappear.