FIre up your smoker for 225 F cooking. Use a few chunks of hickory or a lighter wood.
Season the chuck on all sides with the rub and place onto the smoker.
Smoke until the internal temperature reaches 185 F.
Carefully remove the chuck and wrap in foil. Let rest on your counter for 30 minutes.
Remove the chuck roast from the foil and transfer to a cutting board.
Cut into 3/4" cubes and place into a disposable aluminum pan.
Lightly (very lightly!) drizzle the meat with the BBQ sauce. You just want the flavor from the sauce. Toss gently to coat.
Sprinkle with more of the rub and return to the smoker for 1 1/2 more hours.