Place juices, garlic and seasonings in small food processor or blender container; cover. Process until smooth. Reserve 2 tablespoons for brushing. Place chicken in large resealable plastic bag or glass dish. Add remaining marinade; turn to coat well. Refrigerate 30 minutes or longer for extra flavor.
Prepare grill for indirect medium-low heat (275°F to 300°F). Preheat grill by turning all burners to medium. Turn off burner(s) on one side. Remove chicken from marinade and place on unlit side of grill. Discard any remaining marinade. Close grill.
Grill 40 to 45 minutes or until internal temperature of thickest part of chicken is 165°F, turning occasionally. Move chicken to lit side of grill with skin-side down. Brush with reserved marinade. Turn lit side of grill to high.
Grill, uncovered, 3 to 5 minutes longer or until chicken is charred.