I have 2 Labs... and like any other breed, it depends on the dog -they are all individuals. Buford, my old dog, has had photos done of birds flapping on his head, resting between his paws and cats loving on him. Rio, my young dog, killed 5 of my neighbors chickens over a period of several weeks (they would come over the fence into my yard). The best that I can tell (I don't think like a dog) he didn't maliciously decide to kill them - no open wounds or even mussed feathers - they just didn't survive the "joyful retrieve".
Train your dog... then keep it away from the chickens unsupervised. My chickens will be double fenced (in their own fenced yard within my fenced backyard) and Rio will not be allowed through either gate at anytime - supervised or not.