We demonstrate what is to our knowledge the first realization of an optical parametric amplifier in orientation-patterned GaAs amplifying the emission of a quantum-cascade laser (QCL) with a distributed-feedback (DFB) structure. We report a gain as high as 53 dB at 4.5 mum, in good agreement with theoretical calculations. The narrow spectral linewidth and the good beam quality of this source are imposed by the DFB-QCL, while high-peak-power emission is achieved through the parametric amplification. These characteristics are of valuable interest for long-range spectroscopy.