I'm with the "may not be a hawk" folks. Hawks are our #1 nemesis here. They always kill on the ground and eat them there. Sometimes they chase them under a bush, or pin them by a fence, but I have never had them carry them off. The last one they killed was only a 5 week old cockerel, so it was perfectly small enough to carry. I think you may have a fox or other land predator who prefer the snatch and grab. And foxes are not entirely nocturnal (neither are coyotes who are obnoxious and will stare me down when I encounter them while I'm out running... nature. Gotta love it.)