Combine the first 10 ingredients in a small saucepan; bring to a boil. Remove from heat; cool. Combine lime juice mixture and turkey in a large zip-top plastic bag. Seal and marinate in refrigerator 2 hours. Soak wood chips in water at least 30 minutes. Drain well.
Preheat gas grill to medium-hot (350° to 400°) using both burners. Turn left burner off. Place wood chips in a disposable foil pan or a foil packet pierced with holes on grill over right burner. Remove turkey from marinade; discard marinade. Place turkey, skin side up, on grill rack coated with cooking spray over left burner. Cover and cook 1 1/2 hours. Turn turkey over; cook 15 minutes or until meat thermometer registers 170°. Remove turkey from grill. Cover loosely with foil, and let stand at least 10 minutes before carving. Discard skin.