I had the same problem with my neighbors dogs, but they were very nice about it. Now, first let me say my dog was in on it too. For some reason, he gets in trouble when there are other dogs around. So, the neighbors dog was coming over and climbing ON TOP of the chicken wire that I had over the top of the run and chewing through it until he got enough room to get in. He then proceeded to kill all of my chickens. I went to tell the neighbor that I was getting more chickens and putting an electric fence all the way around my chicken coop (just letting him know his dog might get shocked a few times (I wanted to put it this way instead of saying, "You're dogs causing trouble)). He said "If your husband has a gun, shoot that dog. He said he couldn't because his daughter would kill him. Now, having said all of this, that same dog would also come in our garage and chew up and carry off anything he could find. My neighbor literally would bring me bags back of stuff the dog had carried off. Now back to the point. The neighbor offered to pay for all of my chickens and he got rid of the dog (to a friend, not shooting it).
Oh, by the way, my dog does not bother my chickens now! He lays in the yard with them and actually protects them while they free range!