ChickieDee; a Red tail hawk is absolutely big enough to take one of your chickens. In fact, even a smaller hawk like a Coopers hawk or a Broad wing hawk could kill one- they just wouldn't be able to fly away with it. That flapping wildly at the edge of the lawn that you described is a pretty dead ringer for a hawk trying to "subdue" a good size animal, like your beloved chicken. Sorry to bear bad news.
The best way to prevent hawk attacks on your birds is to have a covered run that the hawk can see. This means if it is something thin, like fine chicken wire or light nylon mesh, you should put streamers, ribbons, bright colored yarn, etc into it. Hawks will drop really fast out of the sky and they might not see a fine mesh covering until it is too late- in which case not only do you end up with a ripped cover, but now you have panicky or injured chickens and a wounded frightened wild animal!
-MTchick