We have had backyard chickens for the past year, a flock of 4 that free range, and so far have lost no birds. Our cats are indoors only, but there are at least 3 neighborhood cats that lurk about in our backyard -- since our lot is the only wooded, shady lot on the block. If anything, I think the cats' presence has warded off more dangerous predators; hawks, coons, and opossums. The cats do seem to enjoy watching the chickens, and the chickens are very nervous about the cats, and tend to flock together in their presence. However, the chickens in a flock, seem to have a formidable power that the cats respect and both groups observe one another from a safe distance and take turns at what has become a communal watering hole in the back (a small pond with plants).
I think your birds will be safe. I initially fretted over the cats also, but a friend with many years' experience with chickens told me that cats + chickens are usually fine, while dogs are the chickens' real enemy. So far, this has been my experience as well.
