Place the goose breasts into a shallow dish, and pour the Worcestershire sauce over them. Cover and refrigerate for 6 hours or overnight.
Melt butter in a large skillet over medium heat. Add celery, onion, goose breasts, and the marinade. Cover, and simmer over low heat for 3 hours. Meat should be very tender, and is great served with the onions, celery and cooking juices right on top.