Combine beer, garlic, brown sugar, red pepper and 1 tbs of the spice mixture in a small saucepan. Bring to a simmer over medium heat. Reduce heat to maintain a low simmer and cook, stirring often, until the sauce is reduced to about 1/4 cup, 20 to 25 minutes.
Pat chicken dry and rub with the remaining spice mixture.
Oil the grill rack. Grill the chicken, until a thermometer registers 155 degrees F about 15 minutes. Brush the chicken with about half of the beer glaze. Grill until slightly charred. Turn the chicken over and brush with the remaining glaze. Grill until slightly charred and a thermometer registers 165 degrees F.