A grill assembly is disclosed which includes a grate having an upper surface configured to support an item of food to be cooked, a cooking chamber, a gas burner or a pellet burner, and a container. The gas burner or pellet burner is adapted to be installed within the cooking chamber and below the grate and to operate using a gaseous fuel or a pellet fuel. The container includes an interior wall, a floor, and an exterior wall adapted to be positioned within the chamber, below the grate, and with the interior wall adjacent the gas burner or the pellet burner. At least one of the interior wall, the floor and the exterior wall of the container defines an opening for allowing a hot gas from the gas or pellet burner to pass into the container. The container can be adapted to hold charcoal and/or wood. The cooking chamber may be formed from an earthen material and can be adapted to support the grate within the cooking chamber.