I've heard of cats going after and killing chickens but usually they will stay away.
It may make a difference if you have multiple chickens together or just a couple... I don't know.
I have five barn cats that give my hens a wide berth. They made the mistake of jumping down into the fenced run when I first had the chickens out there and my hens flew at the cats scaring the tar out of them and sending them scattering.
My cats ignore my chickens now, even when they are free ranging within a few feet of the cats.