Our sweet Lab would love chickens to death off an on. We never punished him for it - he had no idea they were dead. He was such a bouncy fun guy. Our chickens ran loose and he normally ignored them. Once in a while, he'd feel frisky and friendly and would play with them like he would another dog. He'd nudge them with his nose, get them to run, give chase, catch them and take them around the yard to see all of his favorite things. Poor things, they just couldn't take it. It was so sad to see him nudging the poor, dead chicken, trying to wake it up so it could continue to play. There was no mallice in his mind - he was just a BIG HUGE DOG doing what he was bred to do - carry a bird around in his mouth without doing any damage to the body. Sometimes, he'd bring us the bird with a look on his face of "Fix it."
I never considered him a killer. He never killed for fun or hurt the birds physically. Yes, the end result was a dead bird but he only intended to play.
We partially solved it when a neighbor threatened to shoot him for chasing her horse. He wasn't the dog doing the chasing and we knew it (the dog doing the chasing was out when ours was with us) but we knew that our dog would roam the neighborhood to eat any catfood and bird seed he could find. We didn't want him being shot for the dastardly deed of another dog. So, he became an inside dog. He could only go out with someone, or while we were home.
I hope our neighbor's cattle dogs never get loose. They sit by their fence just watching our poultry roam around in our field. Our dogs now don't pay any attention and even our cats ignore the baby chicks running around outside.