At least 1 hour before smoke cooking, soak wood chunks in enough water to cover. Drain before using.
Rinse the inside of the chicken; pat dry with paper towels. Finely shred enough peel from the lemon to equal 2 teaspoons. For rub, in a small bowl combine lemon peel, parsley, salt, pepper, and garlic. Halve the lemon, then squeeze the juice from one half over the entire surface of the chicken. Sprinkle rub evenly over chicken; rub in with your fingers. Place both lemon halves in the chicken cavity. Skewer the neck skin to the back. Tie legs to tail. Twist wing tips under back.
Insert a meat thermometer into the center of an inside thigh muscle, making sure tip does not touch bone.
In a smoker arrange preheated coals, drained wood chunks, and water pan according to the manufacturers directions. Pour water into pan. Place chicken, breast side up, on grill rack over water pan. Cover and smoke for 3-1/4 to 4 hours or until thermometer registers 180 degrees F. Add additional coals and water as needed to maintain temperature and moisture.