Stir together 1/4 cup water and next 10 ingredients; set aside.
Drain wood chips. Place in center of a large square of aluminum foil, and fold edges to seal. Punch several holes in the top of the packet.
Prepare fire by piling charcoal or lava rocks on sides of grill, leaving center empty. Place foil packet on 1 side of coals; place drip pan between coals. Coat food rack with vegetable cooking spray; place on grill.
Arrange chicken, skin side up, over drip pan; grill, covered with grill lid, over medium-high heat (350° to 400°) 10 minutes on each side. Brush chicken with sauce; grill 20 to 25 more minutes or until done, basting and turning frequently.