When it comes to dealing with neighbor's I prefer a direct approach and an attempt to keep things neighborly, whether they've done the same or not. I would go to the neighbor, do not accuse him of complaining, but apologize for the chickens digging up the flower beds and pooping on the deck, or whatever, and state that you will be containing them on your property from now on. It's possible he may be relieved that you are willing to address the problem and still be friendly. Certainly it would have been nice if he had come to you in the first place, but maybe he felt you would take offense. If it doesn't work at least you made the effort and it's well worth it as you may be living next to him for a very long time.