How to Make It
In a saucepan, combine the water, salt, lemon juice, hot sauce, pepper and poultry seasoning and bring to a boil, stirring to dissolve the salt. Let cool to room temperature.
Put 2 chicken halves in each of two 1-gallon resealable plastic bags. Pour half of the brine into each bag, seal and refrigerate for 8 hours.
Drain the chickens and pat dry. Sprinkle all over with the Paprika-Ancho Spice Rub, massaging it into the meat.
Light a charcoal fire in a starter chimney. Add the lit coals to a grill and set it up for indirect grilling: Carefully push the hot coals to the edges all around the grill, leaving a large open space in the center. Place a drip pan in the open space and fill the pan with water. Alternatively, add the lit coals to the firebox of a smoker. Scatter half of the soaked hardwood chips over the coals.
Arrange the chickens, skin side down, on the grill over the drip pan. Cover and cook the chickens for about 1 hour at 250°, rotating them a few times, until the skin is crisp. Turn the chickens skin side up and continue to cook for about 1 1/2 hours longer, rotating them a few times, until an instant-read thermometer inserted in the inner thigh registers 165°. Monitor the grill throughout the smoking process and add more lit coals, soaked hardwood chips and water to the drip pan as needed to maintain the temperature and smoke level. Let the chickens rest for 10 minutes, then serve.
Ask your butcher to remove the backbones and split the chickens in half.