Preheat your smoker to 235°F following your smokers manufacturers instructions, using your favorite wood chips or pellets.
Fill your meat injector with the beef broth. You want to thoroughly jab the roast to get as much broth inside as possible. This will add salt and liquid to the roast and help lock in as much moisture as possible while inside the smoker.
Lightly coat the chuck roast with olive oil. In a bowl mix together the beef rub - onion powder, cayenne pepper, garlic, and salt & pepper to taste and coat the roast.
Place your roast in the foil pan fat side up. This will help keep your roast moist, tender, and flavorsome. This is done by the fat melting down through the meat throughout the cook.
Fill your foil pan with 1 can of your favorite beer (cider or juice) and the remaining beef broth. Again this will help your roast stay moist, tender, and flavorsome. The leftovers also make a fantastic gravy.
Place in your smoker uncovered once your smoker has preheated to 235°F and is burning a clean smoke.
Throughout the cook, you want to check your roast at least once every hour, making sure to baste with the liquid inside the foil.
At the three hour mark, you want to check the internal temperature of the roast and again every hour after thereafter. Check below for your desired cooking temperature. Always remember to get your meat out 5 – 10 degrees under temperature as your smoked chuck roast will keep cooking while resting.
Once at your desired temperature remove the chuck roast from the smoker and wrap in foil. Let rest for 20 minutes. You never want to cut into a piece of meat fresh off the grill. You need to give the meat at least 15 minutes to relax after you remove the roast from the smoker and let the juices rest. This will make the meat far easier to cut, more tender, and well worth the wait.
Once rested slice against the grain and serve!