Remove nad discard giblets and neck from the chicken. Rinse the chicken and pat dry. Place chicken, breast side down, on a cutting board. Cut the chicken, using kitchen shears, along both sides of the backbone, separating the backbone from the chicken. Discard the backbone.
Open the chicken as you would a book. Turn the chicken, breast side up, and press firmly against breastbone with the heel of your hand until the bone cracks. Tuck the wing tips under. Place chicken in a baking dish or pan.
Pulse the garlic and the next 8 ingredients in a food processor until the mixture forms a thick paste. Reserve half of the paste. Rub the remaining half of the paste on both sides of the chicken. Cover the chicken with plastic wrap and chill 1 hour.
Heat one side of the grill to 300° to 350° (medium) heat; leave other side unlit. Place the chicken, breast side down, over the lit side of the grill; top with a piece of aluminum foil. Place a cast-iron skillet on the foil-topped chicken to flatten. Grill, covered with grill lid, 10 to 15 minutes or until the chicken is browned.
Remove the skillet and foil. Turn the chicken over, and transfer to the unlit side of the grill. Grill, covered with grill lid, 45 minutes or until a meat thermometer inserted into the thickest portion of the breast registers 165°. Remove chicken from the grill, and let stand 5 minutes. Brush with the remaining paste.