Add water to the brine bucket. Stir in the rest of the brine ingredients to allow the salt to dissolve.
Submerge the chicken in the brine solution. Cover the bucket and leave it in the refrigerator overnight.
Fire up smoker or grill with rotisserie attachment to 350°F (180°C)
Remove chicken from the brine solution. Rinse with cold water and pat dry with paper towels.
Use butcher’s twine to truss the chicken’s legs and wings, wrapping the twine around the neck cavity and tying a knot.
Combine dry rub ingredients in a small bowl. Use a fork to remove any lumps that may form. Apply rub generously to chicken, working it into any creases and part-way into the cavities.
Pass the rotisserie spit through the chicken cavity, carefully avoiding disturbing the truss. Lock rotisserie spit into place.
Switch on the rotisserie, ensuring it turns freely and smoothly. Close smoker lid and cook until internal temperature is 165°F (75°C), about 1 ½ hour.
Remove chicken from smoker and place on cutting board. Tent in foil and leave to rest for 10 minutes before carving to serve.