I have 3 dogs: 1 rough collie, 1 purebred lab and 1 borador (lab/border collie cross).
The collie used to chase the chickens just for fun, that's because she was just a puppy when I got the chickens. But I spent a few weeks training her to leave them alone and she learned it.
The lab is a different story.... Fist time he saw the chickens, it went into automatic drooling mode!!! And that's what he does every time he sees a chicken, it's sad. He came from a line of champion bird hunters, but he's far from having a soft mouth.
My borador is a rescue, so she might even have some pit in her (who knows...). She's smart enough to seem disinterested on the chickens when we are around, but very into them and we're "not looking".
So far I caught the lab with 1 dead turkey and 2 chickens. The borador is always around when tit happens, while the collie is always by the house and shows no signs of being interested on the killings.
They are all extremely obedient (with the exception of my defiant rough collie, but she's the one I don't have to worry about when it comes to chickens), so I might give it a shot on the "leave it" - they know very well what that means.
I guess I'll have my hands full with my "chicken winter project": teaching my labs to not chase / kill my poultry. This will be fun..... NOT!