Pat the chicken dry with paper towels. Cut away any extra large, long pieces of chicken skin or fat hanging from the thighs. Sprinkle each with the salt, pepper and seasoning.
Preheat a gas grill on high for 10 minutes. Turn one side off and leave the primary burner (and any secondary burners) on medium-high. Using tongs and folded paper towels dipped in vegetable oil, grease the grate over the side that was turned off.
Place the chicken pieces on the cool side of the grill, skin side down. Cover the grill and cook until chicken begins to brown, about 35-40 minutes. Move the chicken closer to the hot side of the grill in a single line if possible. Flip the chicken and baste with the BBQ sauce. Continue to grill, turning and basting every 5 minutes until the chicken becomes crusted, about 20-25 minutes.
Turn the burner(s) down to medium-low (or low if needed to prevent burning) and move the chicken to the hot side of the grill. Baste again and cook, turning frequently, for about 10-15 minutes more or until the internal temperature registers 175F . Discard any remaining sauce not used when basting.
Serve and enjoy!