Are you sure it's a cat? Did you see it take the bird? I've had so many stray cats roam through here and never had one attack a chicken. I've seen them play stalk them, yes, but they seem freaked out when approached by the chickens and give ground to the birds rather than the other way around. It's possible, certainly, that a very hungry stray will take one, especially a chick, but I do think that more stealthy predators get birds and cats are sometimes blamed for it.
The reason I ask is that it may make a difference in how you proceed to capture/ kill the predator.