I had a problem with my very own dog killing chickens. We bought (rescued?) Nahla as a 3 month old pup that was living with her parents in a wretched chicken run/coop. She was filthy dirty and so pitiful, there wasn't a chance we were leaving without her. This was Deliverance-style backwoods country we found ourselves in, wondering aloud on the drive up why we hadn't brought a gun with us.
Anyway, at about 6 months she started killing chickens. Not sport killing, not playing and killing. She ate everything from beak to feet! I couldn't believe it. Considering where she had come from I never thought that she'd bother the chickens. Everyone said she'd never quit and that I'd have to beat her with a dead chicken or tie a dead one around her neck and scare the bejesus out of her.

Of course, I wouldn't do any of those things, so I quit letting the chickens free range for about 6 months. Let them out after that and she's never done it again!
It took me a few days to realize that she wasn't getting her breakfast... Stoli (aptly named) was stealing her food in the morning and Nahla was hungry and took matters into her own paws. The more I think about it the more ridiculous it is. Obviously my own fault there. Sometimes you don't realize what's right in front of you

Because of this, 6 yrs later, I still sit with the dogs at every meal
Bit of a rambley/embarrassing story that I may have told before...