My cats are dedicated hunters who occasionally even kill rabbits and squirrels, but they've been fine with my chickens. In fact it's not uncommon to see them sitting over the chicken feed, surrounded by chickens, waiting for the next squirrel to take a chance at it.
I hatched my own chickens and the cats were very interested in them when the hatchlings first went into their protected run outside, but by the time the birds were big enough to start free ranging the cats had got used to the idea that they weren't prey. Sometimes they'll run through a group of chickens just to see them flap and squawk but they don't try to hunt them. And I have a little call duck who currently lives with the chickens (I think the chickens are keeping her as a pet) and the cats don't bother her either, even though she's as small as other things they hunt.
So my advice is, if you start with grown chickens they'll probably be big enough that the cats won't try to hunt them. If you start with something smaller, then you might keep them in a protected run for a while so the cats get used to them as not-prey, and see you taking care of them.