Preheat your grill to high (500-600 degrees Fahrenheit) and set up for direct grilling.
Using your hands, combine the butter and spice rub in a bowl until combined.
With your finger, gently separate the skin from the meat along the breasts and legs, taking care not to break the skin.
Take half of the butter and spice mixture and form into a ball. Place the ball under the skin. Holding the opened end of the skin down so that the butter doesn’t come back out, use the skin to push the butter over the breasts and legs. Rub the remainder of the butter on the inside of the cavity.
Place the game hen on the grill, and cook with the lid down for about 20 minutes. It’s best to use a thermometer probe to monitor the internal temperature, as these birds cook fast. Cook until the internal temp on the breasts is 165 degrees.
Remove from the heat, and allow to rest for 10 minutes.