  Frequency-stabilized mid-infrared lasers are valuable tools for precision
molecular spectroscopy. However, their implementation remains limited by
complicated stabilization schemes. Here we achieve optical self-locking of a
quantum cascade laser to the resonant leak-out field of a highly mode-matched
two-mirror cavity. The result is a simple approach to achieving ultra-pure
frequencies from high-powered mid-infrared lasers. For short time scales (<0.1
ms), we report a linewidth reduction factor of $3\times10^{-6}$ to a linewidth
of 12 Hz. Furthermore, we demonstrate two-photon cavity-enhanced absorption
spectroscopy of an N$_{2}$O overtone transition near a wavelength of 4.53
$\mu$m.
