Have you talked to your neighbors to see if anybody saw any loose dogs running around? I would talk to everybody in the neighborhood and make sure that all of the dog owners know that their dogs are not welcome on on your property. Be prepared for whoever owns the dog to be in denial. You will know when you have identified the culprit. The owner will say something like, "Oh yeah, Fluffy was out all day yesterday, but he wouldn't do anything like that. He such a good dog that when he gets out he always comes back home. He wouldn't hurt anything. He's so friendly that the most he would do is lick you to death." Dog owners that don't understand the predatory nature of dogs always say their dog would "never" do something bad and that "they would only lick something to death." I don't know why, but they always say those 2 things. Be prepared. The dog (or dogs) will be back. It doesn't have to be a big dog either. Little dogs, especially terriers, can be quite ferocious and some have very strong jaws. I have seen my daughter's Scottish Terrier crush a baseball with one bite. I'm sure that he could tear through chicken wire very easily.
I would strongly recommend that you file a report with the police or Sheriff's Dept. Even if you don't know which dog did it. It will give you a paper trail. If you ever have to shoot a dog on your property, you will have documented evidence that free roaming dogs have been a problem for you. Trust me. That little piece of paper signed by an officer has a lot of weight in a court room. You can also tell your neighbors that law enforcement has been notified and all loose dogs will be suspects.
My neighbors' dog decimated my flock last fall. I sued them and won. I have made it quite clear that if I ever see their stupid dogs on my property again, they will be shot on sight and they will have to pay for any new damages caused by the dogs.
Don't give up. Get more chickens. You have just as much of a right to keep the pets of your choice in your yard as anybody else. The life of a pet dog is not any more valuable or meaningful than the life of any other pet, even a chicken. In the dog's own yard it's a pet. In your yard it's a predator. It's right to live and have a good time killing does not trump your right to keep your chickens safe. If you have to shoot the dog, that was it's owner's choice, not yours. It doesn't matter if it's "not the dog's fault" because you can't shoot the owner and you have to choose which pet gets to live.
edited because I didn't proofread
