Place the chicken on a standing roaster, like this one. If you do not have a standing roaster, you may use a beer can. If using a can, place 1/2 of reserved liquid in the can before inserting can in chicken.
Set chicken in a drip pan. When grill is heated, set the chicken on the cooking grate and add the reserved liquid.
Close the grill and start timing the chicken when the heat rebounds to 375 degrees. Cook for 45 minutes and temp the chicken - it should be cooked to at least 160 degrees. Close grill and continue to cook until internal temperature is reached.