This is so sad. I really feel terrible for you. Once, we got an older dog, (shepherd),and she tried to grab a few chickens. I grabbed her off the ground, and slammed her down, she never saw me coming. Dragged her into the coop yard, made her lay down, belly up, sprinkled corn on her and left the chickens peck the corn. It was the ultimate Alpha dog, humiliation. Believe me, we wore both exhausted afterwards, but I got my message across. Chicken killing can not be tolerated. Many farm dogs have been shot for such an offense. Keep us posted, and good luck.
PS: I will add that I had my foot covering the dog's neck. If she moved, I put pressure on her throat. I was also growling at her, "Are you going to touch a chicken, again? Are yooooooou?" It was extreme, but effective. After that, I would only start pups around the poultry.
I wonder if these flock guardian dogs are so tuned in to sheep, that they still have predatory instincts towards fowl/small animals. After all, what were they supposed to eat when they up in the mountains, with no humans around? They are bred to function independently.