I am not wanting to argue but to help chicken keepers learn what is killing their birds. Most standard mature hens weigh about 4 pounds (think of a white leghorn a smallish standard size hen). Very few hawks will weigh anything near what the white leghorn hen weighs. If you handle a live hawk or even a GHO the first thing that is apparent is how light, and small hawks and owls really are. It is truly impossible for a 4 pound hawk to ever fly away with a 5 pound chicken. No one here has considered the increased drag or wind resistance that a dead chicken imposes on a hawks ability to first get and then to stay airborne.A full grown hawk can carry a chicken no problem.
There are videos on youtube of hawks preying on chickens and if these videos show anything, they show hawks repeatedly trying to and repeatedly failing to fly away with even a smallish chicken. A bantam chicken that only weighs about 20% of what a standard chicken weighs, (about as much as a gray squirrel) is a different matter except for the increased wind resistance or drag a dead chicken creates.
A female red tail hawk could get off the ground with a bantam chicken if there was a strong and steady head wind crossing the she hawks wings to generate lift. But even then there is the problem of drag slowing her down and killing forward momentum. Also any hawk with a large kill in its talons must run to create air speed before getting air borne. How can a she hawk run with both her feet full of dead hen? There are even videos of red tails (our largest hawk) catching small dogs that weigh less than 4 pounds but the hawk was still forced to eat the dog were it lay.