I have a chihuahua/dachshund mix who I do NOT trust with my chickens. I got her from the pound, she was from an abuse case. She is "good" 99% of the time, BUT I will never trust her completely around kids or small animals. The vet tried to clip her nails once and had a difficult time, because she was "like a pit bull" (not my words - that's what the vet said)when they tried to trim her nails! She is my sweetheart dog, but I am always keeping my eye on her!
I do (somewhat) trust my cairn terrier, who by breed history was bred to seek out small animals to kill. My beagle - forget it. Strong prey drive. My cairn/jack russell mix, who knows? He's too hyper!!!
Anyway, my point is that I guess we need to keep in mind that dogs are carnivores. I guess since we feed them and train them, that's what's preventing some dogs from eating them... I don't know that I could ever "train" my chihuahua from not trying to go after my chickens, I guess it's just engrained in her. She stays in when the chickens are out of the coop!