In a small bowl, combine the first seven ingredients; stir in half of the minced garlic. Rub mixture over outside and inside of chicken. Tuck wings under chicken.
Prepare grill for indirect heat. Completely cover all sides of an 8- or 9-in. round baking pan with foil. Place a beer-can chicken rack in pan. Remove 1/3 cup beer from can; save for another use. Using a can opener, make additional large holes in top of can. Insert rosemary and remaining garlic into can. Add beer can to rack.
Place chicken vertically onto rack. Place pan on grill rack. Grill, covered, over indirect medium heat 1-1/4 to 1-1/2 hours or until a thermometer inserted in thigh reads 180°.
Remove pan from grill; tent chicken with foil. Let stand 15 minutes. Carefully remove chicken from rack.