In a large bowl combine water, salt, and corn starch. Add chicken, cover with plastic wrap, and refrigerate 15 minutes, but no longer than an hour.
PREP THE GAS GRILL:
While the chicken brines, preheat the grill. Turn the gas grill on HIGH and close the lid. Preheat the grill for 15 minutes before putting the chicken on.
Scrape and oil the grill grates. Turn off all of the burners except for the main burner, keep that one on HIGH.
PREP THE CHICKEN:
Remove the chicken from the brine and place the chicken on a clean cutting board. Quickly dry chicken with pieces of paper towel.
In a small bowl combine the salt and pepper. Rub the salt and pepper over all sides of the chicken.
Place the chicken on the cooler side of the grill and cover.
Cook for 30-34 minutes, or until the chicken begins to brown.
Position the chicken in a single line close to the main burner that is still on. Brush with BBQ sauce, cover and cook for 5 minutes.
Flip the chicken, brush with BBQ sauce, and cook for 5 minutes. Flip and brush chicken with BBQ two more times.
At this point, the chicken should be crusted with the BBQ sauce and the internal temperature of the breasts should read 165 degrees F. The internal temperature of the drumsticks, thighs, and legs should read 175 degrees F. If the meat doesn’t register these temperatures then close the grill and cook 5 more minutes.
Move chicken to a serving dish and tent with foil for 5 minutes. Serve.
If you like your grilled BBQ chicken to have a little kick to it, then add 1/4 teaspoon of cayenne pepper to the salt and pepper mixture that is rubbed onto the chicken.
This chicken shouldn't stay out for longer than 2 hours at room temperature.
Leftovers will keep in an airtight container in the refrigerator for up to 3 days.