Mix the rub ingredients together in a small bowl.
Rinse the chicken quarters and pat them dry with paper towels.
Then rub the seasoning mixture over the chicken, massaging it into the chicken and let the chicken sit while the grill is preheating.
Preheat the grill over medium high heat (400 degrees Fahrenheit) and turn off the center burners to create an indirect heating source on the grill.
Once the grill is preheated, place the chicken quarters over the section of the grill with the burners off to cook over indirect heat.
Cook for 40-50 minutes (flipping every 10 minutes) until the chicken reaches an internal temperature of 165 degrees Fahrenheit.
Then move the chicken to the direct heat side of the grill. Baste the chicken with the barbecue sauce.
Cook both sides for 2-3 minutes over direct heat to brown and cartelize the skin on the chicken.
Remove the chicken from the grill.
Let it rest for 10-15 minutes. Then the chicken is ready to serve and enjoy!