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.

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.

In a medium bowl, combine celery, lemon juice, salt, pepper and mayonnaise; stir to blend. Add shredded chicken to bowl and fold into mayonnaise mixture. Refrigerate, covered, until chilled and serve as desired.