It's a juvenile Cooper's Hawk, and as Deerman says, these are the archetypal Chicken Hawks. They probably have taken more chickens than any other raptor. Yes they will kill full-size chickens, no problem. At this time of year the juveniles (first-year birds) are moving around in search of new territory, and they are quite happy to settle in on a flock of chickens for a while before moving on.
You can tell Cooper's from Sharpies by the tail. As clearly shown in the second photo, Cooper's have rounded corners on their very long tails, whereas on a Sharp-Shinned it is squared off. There are other, more subtle differences (Cooper's are generally larger, have larger heads and longer necks, and thicker legs) but the tail is the best field mark. Juveniles have the streaked breast and brown back speckled with white; adults are gray with rusty barred chests, very pretty birds.
They are aggressive and persistent predators, specializing in birds. Their short wings are adapted to flying through dense cover - they can crash right through apparently impenetrable trees or brush - and their long legs allow them to reach through brush and grab prey. They attack horizontally, flying low to the ground and zipping around or through bushes and trees.
On the Raptor Migration thread we are discussing ways to discourage hawks. The best way of course is to completely cover your run, but for large areas this is impractical. I've strung monfilament fishing line criss-crossing all over my run and so far, so good.
