Pulse first 12 ingredients in a food processor 20 seconds or until finely chopped. Reserve and chill 1/2 cup of mixture for later use. Place chicken in a large bowl; add remaining mixture, and toss gently to coat. Cover and chill 4 to 8 hours.
Place 3 cups dry applewood chips in center of 1 (18-inch) square piece of heavy-duty aluminum foil; repeat with remaining chips and another piece of foil. Wrap to form 2 envelopes. Pierce several holes in each packet.
Light 1 side of grill, heating to 350° to 400° (medium-high) heat; leave other side unlit. Place 1 applewood smoke packet, with holes facing up, on lit side.
Pat excess moisture from chicken with paper towels, leaving marinade on skin. Sprinkle chicken with desired amount of salt and pepper. Carefully move smoke packet to unlit side of grill. Place chicken over lit side, and grill, without grill lid, 4 to 6 minutes on each side or just until grill marks appear. Transfer chicken, skin side up, back to unlit side of grill; carefully move smoke packet back to lit side for the remainder of cooking. Grill, covered with grill lid and turning pieces occasionally, 1 hour and 30 minutes or until skin is golden brown and meat thermometer inserted into thickest portion registers 165°, replacing smoke packet halfway through. Let stand 10 minutes; serve with reserved sauce.