The police got aholt of AC and removed 2 other killers.... Good thing too, cuz those ones knew I had chickens...
That's a start, but by the time they get notified & have time to respond, your entire flock could be wiped out. I once had a bird dog that I was working. Hadn't had him very long when I found out the hard way that he was a chicken killer...not mine, but a family down the road from me. I paid the lady for her chickens & ducks, and took the dog back to the guy I got him from. Don't know what he did with him, but I've got a good idea.
Some dogs, like the Chihuahua mentioned earlier, can be dissuaded from molesting livestock with some judicious "persuasion". Others, as you've found out, can't. I had a Jack Russell for 12-15 years that killed the first chicken he ever saw; unfortunately, she was one of mine. Me & the dog had a little "discussion" regarding his unacceptable behavior, and he never went after another chicken in his life. In fact, he'd occasionally follow me into the pen, and didn't bother the birds at all. Fortunately, he paid for his first discretion, and never forgot it.
Obviously, your fine neighbors don't seem to care; if they did, you'd never have had the problem, so you've got to do what they should have done long ago.