We announce the identification of a proper motion companion to the star HII 1348, a K5V member of the Pleiades open cluster. The existence of a faint point source 1.1arcsec away from HII 1348 was previously known from adaptive optics imaging by Bouvier et al. However, because of a high likelihood of background star contamination and in the absence of follow-up astrometry, Bouvier et al. tentatively concluded that the candidate companion was not physically associated with HII 1348. We establish the proper motion association of the pair from adaptive optics imaging with the Palomar 5m telescope. Adaptive optics spectroscopy with the integral field spectrograph OSIRIS on the Keck 10m telescope reveals that the companion has a spectral type of M8pm1. According to substellar evolution models, the M8 spectral type resides within the substellar mass regime at the age of the Pleiades. The primary itself is a known double-lined spectroscopic binary, which makes the resolved companion, HII 1348B, the least massive and widest component of this hierarchical triple system and the first substellar companion to a stellar primary in the Pleiades.