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We present a dual-comb spectrometer based on quantum cascade lasers operating at 7.7 µm with a stabilization scheme that enables coherent averaging. We show that by illuminating a low cost near-infrared light source of the front facet of the quantum cascade laser, we can tightly lock one comb line of the dual-comb spectrum, resulting in narrow linewidth with sub-radian integrated phase noise for all RF comb lines.