At least 1 hour before smoke cooking, soak wood chunks in enough water to cover. Drain before using.
For rub, in a small bowl combine the snipped parsley, the lemon peel, and pepper. Remove the neck and giblets from chicken. Sprinkle rub evenly over chicken; rub in with your fingers.
With a sharp knife, cut off the top 1/2 inch of garlic bulb to expose the ends of the individual cloves. Leaving garlic bulb whole, remove any loose, papery outer layers. Place the garlic bulb and lemon wedges in cavity of chicken. Skewer the neck skin to the back. Twist wing tips under back. Tie legs to tail with 100-percent-cotton string. Insert a meat thermometer into the center of an inside thigh muscle without touching bone.
In a smoker, arrange preheated coals, half of the drained wood chunks, and the water pan according to the manufacturer's directions. Pour water into pan. Place chicken, breast side up, on the grill rack over water pan. Cover and smoke for 3-1/4 to 4 hours or until meat thermometer registers 180 degrees F. Add more coals, wood chunks, and water as needed. Remove chicken from smoker. Cover chicken with foil; let stand for 15 minutes before carving.
Remove garlic and lemon wedges from chicken cavity. If desired, season chicken with salt. Garnish with parsley sprigs and additional lemon wedges. Makes 6 to 8 servings.