Hi, I have 3 chickens that are 1 year old, 2 cats that are 7 months old, and 12 chicks that are 2 weeks old. We got the cats to keep the mice out of our coop. (It's actually a shed that we converted to a coop.) Because we had the older chickens before we got the cats, the cats grew up around the chickens and don't go after them. Our roo is 3x the size of the cats! He is not afraid of the cats and the cats have enough respect for him not to bother him. When my husband puts the chickens to bed for the night, the cats follow him to the coop to check on everything. We have the chicks in the house right now, and the cats DO show alot of interest in the chicks. We are trying to introduce the cats to the chicks slowly and under strict supervision so that the cats learn that the new chicks are part of the family. I would say, to answer your question, (as some others have already stated) that it depends on the personalities involved. It would also depend on the size of your chickens. Smaller chickens are more easily preyed upon by any number of preditors, and larger chickens are more likely to be able to defend themselves. Peace and harmony are attainable.
I forgot to mention that I have 6 golden retrievers....bird hunting dogs. They all get along with the chickens and one of our female dogs wants to be mother to the chicks! Natural enemies can live side by side peacefully.