High-precision measurements with molecules may refine our knowledge of various fields of physics, from atmospheric and interstellar physics to the standard model or physics beyond it. Most of them can be cast as absorption frequency measurements, particularly in the mid-infrared 'molecular fingerprint' region, creating the need for narrow-linewidth lasers of well-controlled frequency. Quantum cascade lasers provide a wide spectral coverage anywhere in the mid-infrared, but show substantial free-running frequency fluctuations. Here, we demonstrate that the excellent stability and accuracy of an ultra-stable near-infrared laser, transferred from a metrological institute through a fibre link, can be copied to a quantum cascade laser using an optical frequency comb. The obtained relative stability and accuracy of 2 × 10 −15 and 10 −14 exceed those demonstrated so far with quantum cascade lasers by almost two orders of magnitude. This set-up enables us to measure molecular absorption frequencies with state-of-the-art uncertainties, confirming its potential for ultra-highprecision spectroscopy.M olecules are increasingly being used in precision tests of physics thanks to progress made in controlling molecular degrees of freedom 1,2 . They are now being used, for example, to test fundamental symmetries 3-5 and to measure fundamental constants 6-8 and their possible variation in time 9-11 . Most of these experiments are spectroscopic precision measurements and are often in the mid-infrared (MIR) domain where the molecules exhibit intense and narrow rovibrational transitions. This creates a need for efficient MIR laser sources, prompting efforts to develop ultra-stable and accurate continuous wave (c.w.) lasers as well as MIR frequency combs (refs 12 and 13 for instance). Quantum cascade lasers 14,15 (QCLs) are promising c.w. sources-they are available anywhere in the 3-25 µm MIR range, and each QCL can be tuned over several hundreds of gigahertz. However, their freerunning linewidth of tens to thousands of kilohertz makes their frequency stabilization challenging [16][17][18][19][20][21][22][23][24][25] .Common references used for frequency stabilization in the MIR region include molecular rovibrational absorption lines 3,26 . However, molecular degrees of freedom cannot be controlled as efficiently as atomic ones, leading to limited frequency reproducibility and accuracy. Attempts to develop MIR ultra-stable cavities have been made, but their performances are far from those reported in the near-infrared (NIR) or visible regions 27,28 . It is thus appealing to use the best ultra-stable lasers as frequency references. As these are predominantly in the NIR region, it is necessary to bridge the gap between the NIR and MIR domains. This is possible using an optical frequency comb (OFC). The MIR frequency is locked to a high harmonic of the OFC repetition rate using sum-or difference-frequency generation processes. This not only provides ultimate stabilities of lasers locked to state-of-the-art ultra-stable cavities 29 , but ...