I've seen hawks in my neighborhood once or twice a day, and they're pretty common in where I live. Most of them are relatively small and I've never seen larger hawks. I'm just thinking if I should free-range my flock if I have hawks.
Do hawks of any size kill an adult chicken?
It depends on what type of "small" hawks you have. Sharp-shinned hawks are no threat except to maybe chicks or tiny bantams. Cooper's hawks look quite similar and are somewhat larger. They are small compared to say red tailed hawks or even crows, but they can and will take large adult birds (believe me I know). They prefer to hunt in wooded areas. You may want to spend time learning to ID what kinds you have.
However as long as you free range there is always the possibility of losing birds. If not to hawks, then foxes, dogs, coyotes, bobcats, etc depending on your location.