Season the chicken leg quarters liberally with the BBQ rub on both sides.
Place the chicken on the grill skin-side down.
Let cook for 20 minutes, and then flip over to the other side.
Paint the top of the chicken with BBQ sauce and cook for another 20 minutes.
Check the temperature with an instant-read thermometer.
You want leg quarters to be at least 165°F. 170°F is typically better for bone-in chicken.
Flip the chicken over and paint the bottom with BBQ sauce. Continue cooking until the chicken reaches that ideal temp and then remove from the grill and enjoy.