Yeah, I lay awake at night worrying about the legality of dealing with a chicken-killing critter. So you'd kill a fox, a coyote, a bobcat, a weasel.....but watch a hawk slaughter your chicks?
This is a bit snarky. Personally, I wouldn't kill ANY of the above; I'd make it my business to predator-proof, and accept the responsibility when I lose one due to my lack of foresight.