Combine the ingredients for the marinate and pour over the chicken, covered, in the refrigerator for 3 hour or up to overnight.
Place the chicken on a rack in a pan over lightly dampened hardwood chips. cover tightly and heat in a 450F oven until the smell of smoke is apparent 6 to 8 minutes. smoke for 3 minutes from that point. Transfer the chicken to a baking pan and finish baking (without smoke) in a 350F Oven until cooked through 165F, 10 to 12 minutes more.