Mix the seasonings together in a small bowl and sprinkle onto the chicken halves. Let the seasoned chicken sit, covered, in the refrigerator at least 1 hour and a half before grilling.
Preheat the grill. Place the chicken, bone side down, onto the grill and leave for at least 15 minutes to make sure the seasoning sticks. Gently turn the chicken over and continue to let it cook for another 15 minutes.
Pop the seal of the beer can just enough to spray a fine mist over the chicken without disrupting or extinguishing your flame. If you are using a bottle of beer, use your thumb to control the amount of liquid coming out of the bottle.
Turn the chicken often, using the beer to keep it moist, and making sure not to tear the skin.
Grill until the chicken reaches an internal temperature of 165 degrees F, or its juices run clear, about 1 hour 50 minutes. Remove from the grill and let the chicken rest about 5 minutes before serving.