I do a lot of dog training. For a dog with a strong small-animal prey drive, I don't think you can ever really trust them. But you can have reasonable success with positive reinforcement. One of my pups is a terrier through and through, which means she wants to chase other small animals that scamper across her path (which is why my chickens will be fully fenced away from the dogs). It would be unreasonable for me to try to change her nature, but I have helped her impulse control. With her on leash we will approach an animal in the distance and when she sees it, I call her name, click the clicker (to mark her good behavior, which is looking at me and not the animal) and then I immediately reward with something tasty. Slowly work up to making the game harder, by getting closer to the animals, constantly building on success.
If you keep them leashed on you and keep some cookies in your pocket whenever you deal with the chickens, you'll be ready to reward them when they make good choices. It is all about choices, after all. If they are so engrossed into the animal that they don't "hear" you, you are too close. Get some more distance and try again.
Hope that helps some.
It does help. I just wish that silly dog would mind her own business. She's very stubborn and difficult to train.