In most states, once a chicken enters your yard he becomes your property, and I know for a fact in Florida you can kill them any way you want, my neighbor killed a couple of mine. (Before he decided to move back to the city.....) He shot them off of my fence that separated our properties. And the sherrifs office said they were only chickens, so I'd have to say you're allowed to do want you want with them.
If the chickens doesn't belong to your neighbors then who is going to question you for killing a chicken? And besides I am sure he will make some good stew or maybe some chili!