Soak hickory chips in water at least 30 minutes; drain. Prepare Wet Jerk Rub.
Measure 1/2 cup Wet Jerk Rub, and set aside. Coat chicken with remaining 1 cup Wet Jerk Rub. Place chicken in a large, heavy-duty, zip-top plastic bag; seal bag, and marinate in refrigerator 8 hours.
Preheat gas grill to medium-hot (350° to 400°) using both burners. After preheating, turn left burner off. Place hickory chips in a disposable aluminum foil pan or an aluminum foil packet poked with holes on grill over right burner. Coat grill rack with cooking spray; place on grill over medium-hot coals (350° to 400°). Place chicken on rack over left burner. Grill, uncovered, 30 minutes or until done, turning frequently. Transfer chicken to a platter, and keep warm.
Combine rice and remaining ingredients; toss gently. Spoon rice evenly onto each individual serving plate. Top rice with chicken. Serve immediately. Serve with reserved Wet Jerk Rub.