We demonstrate optical parametric amplification in ZnGeP(2) (ZGP) of the radiation emitted by a single-frequency continuous-wave quantum cascade laser (QCL) in the range 7.8-8.4 μm. The ZGP amplifier is pumped by a single-frequency parametric source at 2210 nm. For a pump energy of 6 mJ, we report an average gain of 50 over this range and a maximum gain of 111 for 7.5 mJ. An exponential trend is observed when changing the pump energy, with very good agreement with theory. These features are of valuable interest for increasing the standoff detection range of hazardous chemicals and explosives by QCL-based backscattering spectroscopy systems.