Unfortunately predators are smart. I have actually read that coyotes have been able to pass along learned information to offspring multiple generations in a row. If a coyote can pass along info through multiple generations, surely a dog or a coyote or a fox or whatever is not going to stop coming to where they've found an easy meal. I am a dog lover, but I wouldn't hesitate to pull the trigger on a dog on our property. Nor would I expect someone else to try and wrangle my dogs up without harming them if they got onto someone else's property and were freaking out their horses or livestock. They're not going to risk their horse getting so freaked out over a dog that it tries to jump a barbed wire fence etc, they're going to shoot the dog. I love my dogs but I also wouldn't want to be stuck footing the bill for the horse vet either. The same applies to neighbors dogs and and your chickens. They need to reimburse you for the cost of the chickens you've lost so far, or at least TOLD how much you're out on the chickens. It is also 100% their responsibility to keep the dog contained and whatever happens on your property is their fault. That being said, you really need to examine your chicken run and coop. You owe it to yourself and your birds to invest in some predator protection. I agree with others in saying that you shouldn't purchase anymore birds until you've got some protection in place. If it's not the neighbors dog, it will be a raccoon or a fox or coyote. Where I live we have mountain lions, hawks, badgers, foxes, coyotes, opossums and at the bottom of the list is the dogs. Check out an electric net system. As I said, predators are smart. Smart enough to know where a free meal is, but also smart enough to know pain. I've never seen a dog get shocked and then go anywhere near an electric net fence ever again.
Just my two cents.