Funnily enough, the BEST chicken dog I have is my Chihuahua.
He is 6 months old and will get a specific bird away from the flock, "hold em" in one corner or whatnot for me to catch that one, and put them to bed at night.
He runs at them, snapping at their heels like a herding dog (only on command) but when he gets too close to one (right in front of his face) he "shuts down" and just stands there. He's amazing. My husband dies laughing watching him "work". He has never put his mouth on one or tried to grab it or anything. But I still wouldn't let him out there with them alone. Just that he has any kind of prey drive shows me that he has the capability to snap at one. I say "Max, hit the deck!" though and he calls off and hits the ground instantly in a down stay. He is so smart it isn't funny.
My lab has NO prey drive at all. Which is why I trust him. Squirrels and other small animals have walked right up to him and he doesn't move or make a sound. He just doesn't care. Couple that with his impeccable manners (rock solid recalls, leave its, directional commands, retrieves, downs, stays, sits, etc.) and I have a solid dog that I believe will never bother my birds.