Preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with aluminum foil.
Place chicken breasts on prepared baking sheet.
Cook in the preheated oven until no longer pink in the middle and juices run clear, 15 to 25 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Shred chicken breasts.
Stir chicken, avocado, scallions, celery, onion, lime juice, cilantro, cayenne pepper, salt, and black pepper together in a bowl.