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A cat that's a year old is no longer a kitten. That's a full grown cat.
You're right though, it depends on the cat.
Most house cats, even most that live outside, or barn cats, won't bother them. I have 9 cats, several hang around the coop to hunt mice. A couple like to run through groups of chickens and scatter them sometimes, (and then watch and snicker, "ha ha, made you jump!") but these are also the same cats that don't want to go out the back door if there are chickens gathered there. They run from the chickens more than they run at them.
I have about 30 chicks of various ages running around the cats aren't bothering them either. However, these have had mama hens to protect them, too. When I incubate chicks, and they don't have a mom to protect them, I keep them confined, away from cats and everything else, until they're at least fully feathered out. Then they seem just fine. I would bet on even my cats not eating a brand new fuzzy chick.
I have heard of cats that will attack and kill a full-grown chicken. So You just have to see what your individual cats do. They'll most likely be just fine, but test them out and see, is all you can do.