When other options aren't available, e.g., dog only circling run, dog only sniffing at fence, non-threatening dog that can be captured and leashed (always take pics/vid of activity). and one impulsively/deliberately acts to prevent the cur from taking a third hen in its mouth and shaking its life out???
Call the cops and complain that you went to protect the chickens and the dog turned on YOU. Yes, chickens are so much ho-hum to both the dog owner & most cops. However, there isn't one State in this great nation that doesn't allow a human to kill a strange dog that even "seems" to be turning on one, on one's own property.
Cops will take a report & the dog owner will be more worried about being sued to pay for one's PTSD treatments than giving one lip about "they were just chickens!!!"
Won't work for everyone, but it certainly works, here. Also, if one is in a rural area and you know who owns the dog(s) that appear most often? Very politely knock on their door and inform them that "gee, I know your dog likes to wander, but I've had to put out poison for the coyotes killing our chickens and I'd sure hate it if your dog got a hold of it - so, please, keep it(them) on your property." Has also been an effective tactic.
Remember, a loose dog is nothing more than road kill waiting to happen.
I like dogs, don't like some dog owners.