We developed a high-precision spectroscopic system at 8.6 μm based on direct heterodyne detection and phase-locking of a room-temperature quantum-cascade-laser against an harmonic, 250-MHz mid-IR frequency comb obtained by difference-frequency generation. The ∼30 dB signal-to-noise ratio of the detected beat-note together with the achieved closed-loop locking bandwidth of ∼500 kHz allows for a residual integrated phase noise of 0.78 rad (1 Hz–5 MHz), for an ultimate resolution of ∼21 kHz, limited by the measured linewidth of the mid-IR comb. The system was used to perform absolute measurement of line-center frequencies for the rotational components of the ν2 vibrational band of N2O, with a relative precision of 3×10−10.