In a very large bowl, mix together everything except the chicken to dissolve the salt and sugar in the brine.
Add the chicken and cover the bowl with cling wrap. Place in refrigerator and let sit for at least 30 minutes and up to two hours in the brine.
Remove the chicken from the brine and pat it dry with paper towels.
Preheat the grill and rub the grill grate with oil to prevent sticking.
Grill chicken pieces skin side up for six minutes, then turn the chicken over and grill for another six minutes.
Move chicken pieces to an area on the grill that is not directly over heat, baste with bbq sauce, close cover and cook for 10 minutes.
Turn chicken, baste with sauce again, close cover and cook another 10 minutes.
Check temperature of chicken pieces near the bone with an instant read thermometer. When the internal temperature reaches 160º F, the chicken is done.
Remove chicken pieces from the grill to a clean plate, loosely cover with foil to keep warm and let chicken rest for five minutes before serving.