Clean chicken well. Remove back bone, then flatten breast bone. Place chicken quarters in glass dish.
To make marinade, combine lemon juice, honey, oil, and garlic in blender. Process for 30 seconds. Remove to a bowl, stir in chopped basil and pepper and pour over the chicken. Cover and refrigerate at least 6 hours or overnight, turning chicken a few times to coat.
To cook, remove chicken from marinade. Place legs and thighs 3-4 inches over medium-hot coals and grill for 10 minutes, turning once. Add breasts to grill and cook 30 minutes, turning and basting every 10 minutes. When crisp, remove and serve with fresh basil on side.
