If using raw chicken, place chicken breasts in large skillet and cover chicken with chicken broth. Place skillet over medium-high heat and bring liquid to boil, then reduce heat to low.
Cover skillet and simmer chicken 20 to 25 minutes or until chicken breasts are cooked through, reading 165° Fahrenheit when checked with an internal thermometer. Remove chicken from skillet and set broth aside.
Shred chicken using desired method from Notes below.
Place shredded chicken in large bowl (if not already in one) and add dry rub, mayo, BBQ sauce, celery, onion, pepper, and salt. Stir well to combine ingredients.
Once combined, stir in reserved chicken broth in 1 tablespoon increments until mixture is as creamy as desired. Note: I typically use between 2 to 4 tablespoons chicken broth.
Sprinkle additional dry rub over chicken salad if desired. Serve immediately or cover bowl and refrigerate at least 30 minutes, then serve with buns, lettuce cups, crackers, or as-is.