Bring chuck roast to room temperature. Pat dry with paper towels and place on a baking sheet.
Coat roast with olive oil, rubbing over all sides.
In a bowl, combine brown sugar with garlic, onion powder, onion flakes, rosemary, smoked paprika, salt, pepper and dry mustard.
Sprinkle all over roast and press into the roast.
Set roast aside and prepare a grill fire.
Add hickory or pecan chunks and heat grill to 400°.
Place roast over indirect heat and close the grill lid. Lower temperature to 350°.
Cook roast for 45 minutes. Check internal temperature with a grill thermometer, cooking until about 155° for medium doneness.
To cook until fall apart tender: place roast in a pan and cover with 2 cups beef broth, cover with foil and continue to cook on the grill or in oven for 30 minutes or until roast reaches 190° - 205°.
Rest roast for 15 minutes before slicing thin.