They won't kill the chickens...if they do you are more than capable of suing. Be blunt. When somebody approaches you with a threat, you call their bluff. If this guy wants to act like a complete jackass and pay you his life savings because he wants to kill your chickens, so be it. Also, if the threats are bothersome (even if they are against the chickens) you should immediately file a police report. My father has been a cop for 28 years. When people would threaten dogs for being on property or whatnot, the owner would file a report, so if the dog went missing or was injured there would be immediately probable cause. I would certainly contact authorities and let them know you, and your property, have been threatened. Also, it isn't your fault. He threw off the neighborhood chemistry first.