Prepare a hot grill outside or preheat a grill pan to high heat. Preheat oven to 375°F.
Toss raw chicken in a bowl with rub, a few pieces at a time, until all chicken is well-coated. Grill chicken on well-oiled grill or grill pan for about 2 minutes on each side, until nice grill marks are formed. If chicken pieces are very thick, finish cooking for 5-10 minutes more in the preheated oven. Allow chicken to cool a few minutes and then pull apart into nice shreds. Toss chicken with BBQ sauce so that it is well-coated but not overly wet. Keep warm in a warm saute pan until ready to use.