Combine the ingredients for the brine solution until the salt looks dissolved. Place the chicken in a gallon plastic baggie and add the brine solution. Do this a few hours prior to cooking; overnight is best. Refrigerate.
Remove the chicken from the brine and discard bag. Rinse the brine off the chicken and pat dry.
Preheat an outdoor grill. Spray grates with cooking spray then add chicken. Using a basting brush, brush the barbecue sauce on the chicken. Turn the chicken after about 5 minutes and baste the other side in sauce. Do this again until each side has been basted 2 or 3 times and chicken is done. Internal temp should read 165 for chicken.