We are getting a Great Pyrenees this coming Spring as a puppy to be a LGD on our farm she will be raised outside to the point the animal will want to stay outside to run its boundaries for danger. We are buying from a family that has these dogs as working dogs the puppies will be raised by the parents and introduced to chickens, ducks, sheep, cows you name it. They will learn quickly by their parents that these are not toys to chase. These dogs are bred to be guard dogs so for yours to be actually chasing another animal clearly means this is not why you bought the dog in the first place. They make wonderful pets but their instinct is to protect. I really don't know how you can get a adult dog from stopping this behavior as a puppy they learn right away that this is something I need to guard and take care off.
You could try leash training where he drags a leash around and if he runs after the chickens/ducks he gets corrected with a NO Chase. But how he will understand to protect from this point I am not sure. This is for a dog trainer to deal with.