Rinse brisket thoroughly under cold water and pat dry with paper towels. In a small bowl, mix together House Seasoning, chili powder, brown sugar, onion powder, oregano and cayenne. Rub brisket with the rub on all sides.
Follow directions on your grill/smoker for indirect grilling. Place the soaked chips into the chip box, or make a pouch with tin foil for the chips, then place pouch directly on the coals. Place brisket fat side up in a large disposable aluminum pan and place in the center of the grate and cover the grill.
Slow grill the brisket until tender and an instant-read thermometer inserted in the center of the meat reads about 190°, about 6 hours. Add coals and wood chips as necessary to maintain a constant temperature. Transfer the brisket to a cutting board to rest for about 10 minutes. Slice the brisket across the grain and serve.