If your cat actually has decided to kill and transport chickens, punishment after the fact won't fix his behavior. Instant negative feedback DURING the bad behavior might matter to him, but nothing after the fact will relate to the joy he feels during the hunt and kill. If he's actually the culprit, rehoming him to a chickenless place, not nearby, is the alternative. Many rescue groups are out there, and with full disclosure, maybe another home can be found for him.
Did you catch him killing a chicken? Is it possible that he's taken over another critter's stash? Of course he'll be grad to eat chickens, and probably kill chicks, but most cats won't take on big birds.
Mary