At least 1 hour before grilling, soak wood chips in enough water to cover.
Trim fat from brisket. Brush brisket with oil. For rub, in a small bowl stir together paprika, salt, black pepper, cayenne pepper, and thyme. Sprinkle rub evenly over all sides of meat; rub in with your fingers.
Drain wood chips. For a charcoal grill, arrange medium-low coals around a drip pan. Test for low heat above pan. Sprinkle some of the drained chips over the coals.
Place brisket on grill rack over drip pan. Cover and grill for 3 to 3¾ hours or until meat is tender. Add more wood chips every 30 minutes. (For a gas grill, preheat grill. Reduce heat to low. Adjust for indirect cooking. Add wood chips according to manufacturer's directions. Place meat on a rack in a roasting pan; place pan on grill rack over burner that is off. Grill as above.)
Meanwhile, warm bottled barbeque sauce in a saucepan over low heat. Let meat stand for 10 minutes.
To serve, slice meat thinly across the grain. Serve with barbeque sauce. Enjoy!