Doesn't matter if it has wolf or not it a dog your chickens are livestock also known a part of the food chain so if you do something to the dog you will be in trouble just saying and by the sound of these neighbors just might do something back to you so keep that in mind.
I disagree. In the areas where I have lived, chickens are considered livestock and the property owner can protect his livestock with deadly force against roaming dogs on his property attacking said livestock. If you hurt the animal (shoot them with a BB and simply injure them) you are in trouble for animal cruelty; but if you shoot to kill, you are well within your rights as the property owner.