Boil chicken: Place chicken breasts in a large Dutch oven, then pour chicken broth over them and add thyme sprigs. Bring mixture to a boil over medium high heat, and cook, 15 minutes, or until chicken is done and registers 160°F on a meat thermometer inserted in the thickest portion of the breast meat. Remove from heat and allow mixture to cool to room temperature for 45 minutes to 1 hour.
Shred chicken: Remove chicken breasts from broth and reserve broth for another use. Broth can be transferred to containers and frozen, if desired. Place chicken breasts on a work surface and remove, then discard skin and bones. Meat will shred easily with fingers, as it should be very tender. You will have 5-6 cups of shredded chicken.
Make dressing: In a medium bowl, combine celery, lemon juice, salt, pepper and mayonnaise; stir to blend.
