Chickens are usually too big for a cat to tackle. Cats are territorial animals and will help run-off other predators as well as other cats. In some cases cats can even be quite scared of chickens and there are several keepers who have seen.
All cats do not attack chickens but unfortunately there are some that will. Most chicken farmers know to keep cats away from their hens and chicks. Cats will pick with a chicken that is not scary and weak. For this reason baby chicks.