Sprinkle and rub seasonings thoroughly all over the chuck roast. Generously coat all sides by pressing the seasonings on.
Preheat your smoker to 225 degrees Fahrenheit.
Place the seasoned chuck roast in the smoker. Insert a meat probe into the thickest part of the roast.
Smoke until the internal temperature reaches 165 degrees Fahrenheit, about 3-4 hours depending on its size, spritzing with apple juice every 45 minutes.
Remove the roast from the smoker and wrap it tightly in butcher paper.
Return it to the smoker and continue to cook until the internal temperature reaches 200 degrees Fahrenheit, about 1-2 hours.
Remove the roast from the smoker and let it rest for at least 30 minutes before slicing to allow the juices to redistribute throughout the meat. Serve with BBQ sauce.