Add the chicken, chicken broth, celery, parsley, bay leaves and salt in a 6-quart or larger slow cooker. Cover and cook until the chicken shreds easily with 2 forks. About 3 to 4 hours on high or 4 to 6 hours low.
Remove the chicken, discard the solids, you can save the broth for another use, if desired. Shred the chicken with two forks and refrigerate for up to 4 days or freeze up to 3 months.