Place chicken, celery, onion, garlic, and chicken broth in slow cooker.
Cover and cook on low 6 hours.
Remove chicken from slow cooker and shred.
Drain cooking liquid, reserving 1/2 cup; discard solids.
Toss chicken with reserved 1/2 cup broth.
Return to slow cooker and mix in wing sauce.
Cover and cook on low 30 more minutes.