My assumption would be a bait poison. They are popular and the rat searching for water would be my biggest clue as that is common for bait poison from what the pest control company told me. The rats carcass was next to their water. I don't know about the chickens body placement. I should ask her and get back to you all.Long shot, but I'll ask anyway. Do you know what poison was being used? Exactly?
I myself wont use bait because we have dogs and cats and chickens... and the pros don't recommend if you have other animals (plus I live on a small island and all things have an impact). At our cabin up Koke'e we used an electric mouse trap that worked great. Reusable and all of the good stuff especially if you don't mind the manor of death. he he!