A unipolar injection quantum cascade (QC) laser grown in an AlGaAs/GaAs material system by molecular beam epitaxy, is reported. The active material is a 30 period sequence of injectors/active regions made from Al0.33Ga0.67As/GaAs-coupled quantum wells. For this device a special waveguide design, which complies with a GaAs heavily doped substrate and very short Al0.90Ga0.10As cladding layers, has been optimized. At a heat-sink temperature of 77 K, the laser emission wavelength is 9.4 μm with peak optical power exceeding 70 mW and the threshold current density is 7.3 kA/cm2. The maximum operating temperature is 140 K. This work experimentally demonstrates the general validity of QC laser principles by showing laser action in a heterostructure material different from the one used until now.