Surface-emitting distributed feedback quantum-cascade lasers operating at \lambda \approx 7.8 \mu m are demonstrated. The metal-covered second-order grating is shallow-etched into the surface of a thin InGaAs contact and cladding layer. This forms a hybrid waveguide and used to achieve relatively low waveguide losses and high coupling strengths. The devices exhibit stable single-mode operation from 90 to 130 K with a side mode suppression ratio above 20 dB. A slope efficiency of 194 mW/A is obtained at 90 K, which is twice higher than that of the Fabry-Perot counterpart.