Pullet chasing around the cats?

We have indoor/outdoor cats who generally leave the chickens alone. Every once in awhile, we have found them in the coop laying among the chickens and we have never witnessed them trying to chase or hunt the chickens. Recently however, a 19 week old Polish pullet has been chasing the cats away from the coop, which is fine by us. In the last few days though, she will see them across the yard and run away from the flock in order to chase the cats around. Usually the cats have no idea what to do and run away but yesterday I watched our big male cat run away for a little while and when the chicken pursued, he turned around and swiped at her. Frankly I don't blame him. This morning I watched this pullet chase a cat across our entire property until the cat found a tree. It isn't happening every time she sees a cat but I see it frequently enough. She is a super friendly pullet and hasn't shown any aggression problems otherwise. However, I am worried that at one point either a cat or a chicken will end up being hurt if this continues. She leaves the dogs and all other chickens and ducks alone. Has anyone ever have this happen? Should I expect this to go away once she begins laying? Any methods to stop this?

Perhaps she once experienced a cat being aggressive toward her or another chicken and she's become aggressive to them in response.
Clearly, something in her past makes her think cats are her enemy.
I would worry that eventually a cat will kill a chicken. They are bigger predators than chickens are.