IMO, when it's a neighbor's dog and if possible, the best thing to do is to catch or trap the dog and take it to the shelter, repeat as needed.
Good, non lethal strategy. As was the person who suggested 'paintball gun' to send the owner 'a message'.
I think though, paintball gun, or even threats of "come pick up your dead dog" will ultimately lead to neighbour war - because of the mentality of the dog owner. Let's face it, dog owner is too dumb to have dogs, possibly even to exist himself. But it is the whole "all types make up the world" thing. Unfortunately, there are stupid people, and dangerous people, and sometimes that goes together.
The beauty about the "calling the pound" strategy is that you get taken out of the mix. Focus then goes onto animal control and fines paid. And those neighbours won't want to pay the fine (motivation for irresponsible people), not that I am really pro-govt/pro-bureaucracy.
As others suggested, make your chickens more secure - from other predators. Basically, everything wants to eat chicken. If the neighbour's dog can get them, then the local foxes, coyotes, eagles, hawks, and everything else can get them too. It really is unpleasant to come across a pile of feathers that was, a short time before, a lovely little hen with personality. My brother-in-law and I did the 'forensic' investigation on the five massacred by foxes, with mother and cubs likely the culprits. At least three, maybe four involved.
So my vote would be the animal control route if you can either catch it or they can respond. The paintball option if not possible. And sure up your feathered babies regardless.