The Solar Neighborhood XXX: Fomalhaut C

LP 876-10 is a nearby active M4 dwarf in Aquarius at a distance of 7.6 pc. The star is a new addition to the 10-pc census, with a parallax measured via the Research Consortium on Nearby Stars (RECONS) astrometric survey on the Small & Moderate Aperture Research Telescope System's (SMARTS) 0.9-m telescope. We demonstrate that the astrometry, radial velocity, and photometric data for LP 876-10 are consistent with the star being a third, bound, stellar component to the Fomalhaut multiple system, despite the star lying nearly 6 degrees away from Fomalhaut A in the sky. The 3D separation of LP 876-10 from Fomalhaut is only 0.77+-0.01 pc, and 0.987+-0.006 pc from TW PsA (Fomalhaut B), well within the estimated tidal radius of the Fomalhaut system (1.9 pc). LP 876-10 shares the motion of Fomalhaut within ~1 km/s, and we estimate an interloper probability of ~10^{-5}. Neither our echelle spectroscopy nor astrometry are able to confirm the close companion to LP 876-10 reported in the Washington Double Star Catalog (WSI 138). We argue that the Castor Moving Group to which the Fomalhaut system purportedly belongs, is likely to be a dynamical stream, and hence membership to the group does not provide useful age constraints for group members. LP 876-10 (Fomalhaut C) has now risen from obscurity to become a rare example of a field M dwarf with well-constrained age (440+-40 Myr) and metallicity. Besides harboring a debris disk system and candidate planet, Fomalhaut now has two of the widest known stellar companions.