Hmmmm...I might worry more about the lab puppy. But the above posts were spot on - depends on the cat. I have never had a cat hurt a chicken - in fact, they have always shown them tremendous respect and even my ferals (who I eventually tamed, spayed/neutered etc.), actually bonded with them beautifully. I would find them laying down by the chickens purring and happy (feeling like they had a family?). I believe those cats would have protected the chickens if they had needed protection. One of the former ferals loved my feathered friends so much that when hen Betty would run up to him and catch his tail in her beak (to amuse herself I think!) he would just let her and stand still till she let go! Then he'd lay down by her and purr.
With all the cats I've had or fostered, once they understood that the chickens were my "family" they showed respect. They would see me treat the chickens in the same loving way I treated them and that's all I had to do. Even worked with the squirrels. At first my cats went after them like I suppose any self respecting cat would. But once they saw that I liked the squirrels, even fed the squirrels, they stopped and now hang out together peacefully. It's been quite interesting!
That said, I have read posts on BYC where people have had problems with cats so observation and caution are certainly wise. I know not every situation is this tame. You are smart to have asked the question.