A motor vehicle brake system includes a master brake cylinder actuatable by a brake pedal and having only one pressure chamber; an electrically controllable pressure supply device; a pressure medium reservoir, under atmospheric pressure from which the master brake cylinder and the pressure supply device are supplied with pressure medium; and at least two hydraulically actuatable wheel brakes. The wheel brakes can be actuated by the master brake cylinder or by the pressure supply device. The pressure chamber of the master brake cylinder is separably connected via an isolating valve to a first brake circuit supply line. The wheel brakes are divided into at least two wheel brake groups. The first wheel brake group connected to the first brake circuit supply line, and the pressure supply device connected to a second brake circuit supply line to which the second wheel brake group is connected.