Unless you have very young and motherless chicks I wouldn't be worried about the cat. I had a semi feral tom spending hours lying in my coop once. He was after the mice the chicken's feed attracted. I had no chicks. He and the chooks got along fine. Then I bought some young chicks and had to run him out of there for 4 months. Once they were grown some? He came back and again hunted rats and mice. No problems.
So, if you have any chicks then it can be a worry but other than that? Chickens will sometimes gang up on an aggressive cat and pound the heck out of him. They terrorize my 6 lb Yorkie pup if she goes anywhere near the run while happily cohabiting with my 19 lb Maine Coon who is also after the mice and rats.