Whisk together first 3 ingredients. Reserve 1 cup sauce; cover and chill remaining sauce.
Arrange chicken in a shallow dish. Pour reserved 1 cup sauce over chicken, turning to coat. Cover and chill 8 hours, turning chicken once.
Remove chicken from marinade, discarding marinade.
Prepare a hot fire by piling charcoal or lava rocks on one side of grill, leaving other side empty. (For gas grills, light only one side.) Place food rack on grill. Arrange chicken over empty side (unlit side of gas grill), and grill, covered with grill lid, 1 hour or until done, turning once.