Slightly flatten the chicken halves and place them in a 3-quart rectangular baking dish. In a blender or food processor, blend or process the garlic and salt to make a paste. With blender or processor running, slowly add olive oil. Pour the oil mixture over chicken halves, turning chicken to coat both sides. Loosen breast skin and rub oil mixture under skin. Cover and refrigerate for 2 to 24 hours.
For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above the pan. Place chicken, bone side down, on grill rack over drip pan. Cover and grill for 50 to 60 minutes or until chicken is no longer pink (180 degrees F). (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Grill as above.) Serve chicken with lemon wedges. Makes 4 servings.