This is a hard one for me, as a poultry owner and a dog owner I am on the fence. I have had the dog from next store chase my birds "lucky my ducks can fly", anyway I wouldnt shoot him. I raise hunting dogs and like it or not I have had dogs get out and run, and I wouldn't want anyone shooting my dogs. But then again if they killed someones fowl or did damage I would be happy to replace it or its value. Then again I keep my birds protected and only allowed out when I'm home so I don't have to worry about these kind of things, so although you have the right to shoot the dog, its all down to the dogs owner. Where I live its a $60 dollar fine to let you dogs run loose and all a person needs is a photo of your dog off leach without you being their. If I were you I'd check into that and if its the same where you live I'd keep my birds penned up and just keep taking photos of the dog and sending them in. After a while of getting fines I bet your neighbor will think twice, or if its legal for you, you could just shoot the dog.