Agree with much of what has been said here regarding this poor dog & your post is very telling. You mention that the dog is bonded to you, your poodle, the 1st pot bellied pig, etc. That should tell you that all those 'original cast members' are who she has bonded to & she will protect those beings from anything else that intrudes: chickens, other dogs, other people, etc. After raising LGDs for a decade & reading voraciously on the topic, I can tell you that the bonding of an LGD with its intended social group (those whom it will protect & serve) occurs primarily at 2-4 mos old, trailing off at 5-6 mos. Then that learning window pretty much closes. Also, the maturity of an LGD is very slow in relation to its lifespan....it takes 18 mos-2yrs for a dog to fully mature & most only live about 10 years. So your girl is just coming out of puppyhood when behavioral mistakes are common because energy is high (& supervision should be equally as high). I think it would be a crime to muzzle & tie up this dog, to punish her for simply doing what she has been conditioned and allowed to do: she is protecting the ones that she bonded to first & she has a lot of energy to spend (even tied up) so she catches whatever she can (a chicken in this case) to play with & pass the time.
Respectfully, you do not have an LGD. You really didn't have one when you brought her home at over 6 mos old & put her in the backyard. You have a large family pet that you should immediately take through a basic obedience training course so that you can keep her future behavior in check. She should also receive lots of exercise outside the backyard to give her an outlet for her youthful energy. You should not expect her to guard anything other than your family & your poodle. Remove the chickens from your yard or you will slowly lose them all to her. Not out of malice. Just because she doesn't view them as something to protect. ALL of these changes will make her a happier dog & you will be a happier dog owner in the long run.
With regard to a previous posting, most any dog can NOT be trained to do most anything. I have a border collie that will never be able to do the job my LGD does & vice versa, even as smart as she is. Great Pyrs have guarding in their genetics but the deck was stacked against you when you got yours at over 6 mos old because she was already too old to do the best job of bonding with any livestock. Once you primarily bond an LGD to people, they won't really care about or want to go out with livestock. My LGDs never see the inside of my house. They never leave the pastures that are home to the flocks they guard. The vet comes here to vaccinate them in the fields. They eat, sleep, play & live among the herds & flocks that are theirs to guard. They love my family members b/c we come out to feed, pet & play with them daily. They are loving animals to us but they know where their place is and most of them won't even come out the gate when called. They guard their animals ferociously against anything that trespasses into their territory.
I would advise to enjoy your Great Pyr pet & love her for what she CAN do for you, not punish her for what she can't.
Good luck.