Great Pyrenees are also herding dogs and used in many places around animals. Guess you just can never be sure at the end of the day....I am sorry you lost your pullet and feel so disappointed in your dog.
To me this seems to be an unfavourable mix as the Husky is well known for a strong prey drive and obstinacy and Great Pyrenees for their independent spirit and love of freedom.
She is around those chickens every day, with the fence between them... She ignores them... She doesn't run at the fence or act interested in the chickens at all. They frequently take dirt baths behind the pavilion right next to the fence and she could care less.... She is FAR more interested in squirrels and moles.
But I never trusted her completely which is why I've never allowed her outside of the yard without being on a leash.
Clearly now I have two critical actions I must take -
1. Find a way to keep the chickens from flying into the backyard
2. Find a way to teach her not to kill chickens.
I feel much more certain about the 1st one than the 2nd.....