In our area, you can call animal control and they can seize the dog until either a fine is paid or a verbal warning (depending on how many times), and they will do it in the name of unleashed dog, not dog eating chickens. In Maine you can shoot a dog if it is harassing your livestock. I would catch him, and bring him to the local shelter. THey'll have to pay a loose dog fee and learn to keep him/her tied up or fenced in without even involving you. If they are reasonable and you can talk with them start there. If not, quietly, catch him or scare him off, or call animal control. Keep a long loop leash around for next time. He may be a person biter too! In Maine people take this seriously so it would go to court and a dog can be ordered euthanized worst case scenario, or muzzled, or the court can rule they have to put up a fort to keep their dog in. Their cost, their responsibility.
Since I train dogs and am a vet tech first I would advise to talk to him or go animal control route. I hate seeing dogs with pellets in them, it sucks surgery wise. But if they're asshats and can't understand their dog is their responsibility, the shelter would be my next suggestion. I have three dogs and somehow they don't eat our chickens!! We keep our dogs under very tight reigns. If a loose dog came by my house, to harass my dogs or my chickens, they'd get scared away....scared enough to never come back...
If you call ACO or the shelter, ask to remain anonymous. Whos to say hes not harassing other neighbors in your area? Unfortunately in the dog mind this is a self rewarding behavior so training him to NOT eat chickens is very hard and very time consuming. Its better to manage it as an owner, just in case.