Soak hickory or pecan wood chips in water at least 30 minutes. Drain.
Whisk together basil and next 4 ingredients in a shallow dish; add chicken. Cover and let stand 30 minutes at room temperature.
Prepare a hot fire by piling charcoal in center of grill; let burn 15 to 20 minutes or until coals are gray. Place wood chips on charcoal. Spray cold cooking grate with cooking spray; place on grill.
Remove chicken from marinade, discarding marinade; arrange chicken on cooking grate, and grill, covered with grill lid, 30 to 40 minutes or until meat thermometer inserted into thickest portion registers 180°, turning occasionally. Remove chicken, and let cool completely before slicing.