Dual-comb spectroscopy performed in the mid-infrared-where molecules have their strongest rotovibrational absorption lines-offers the promise of high spectral resolution broadband spectroscopy with very short acquisition times (μs) and no moving parts. Recently, we demonstrated frequency comb operation of a quantum-cascade-laser. We now use that device in a compact, dual-comb spectrometer. The noise properties of the heterodyne beat are close to the shot noise limit. Broadband (15 cm(-1)) high-resolution (80 MHz) absorption spectroscopy of both a GaAs etalon and water vapour is demonstrated, showing the potential of quantum-cascade-laser frequency combs as the basis for a compact, all solid-state, broadband chemical sensor.