1Heat gas or charcoal grill for indirect cooking. Carefully brush grill rack with vegetable oil. Place chicken, skin side down, on grill. Cover; cook 15 minutes. Turn chicken skin side up. Cover; cook 20 to 30 minutes longer, turning occasionally, until juice of chicken is clear when thickest pieces are cut to bone (at least 165°F).
2In small bowl, mix remaining ingredients. Brush chicken with some of the glaze. Cover; cook 3 to 5 minutes, skin side down, until deep golden brown. Remove chicken from grill to platter. Brush with remaining glaze.