Season the Chuck Roast aggressively on both sides and set the smoker to 225 degrees F.
Smoke the Chuck Roast for 2 hours before checking to see if the rub has adhered to the roast. Combine beer, worchestersire and apple cider vinegar and mop onto the roast once an hour until the roast has reached an internal temperature of 170 degrees F.
Place Chuck Roast in an Aluminum Half pan and pour in about 1 cup of the mop mixture. cover with foil and braise for about 2 hours. To cook faster you can raise the temperature at this point as high as 275 degrees F.
Once the internal temp has reached 200 degrees F. use the probe thermometer to check for tenderness. If done, cover and rest the roast in the braising liquids with a few tablespoons of butter on top of the roast for 15 minutes. Slice against the grains in pencil thick slices.