We report the discovery of a brown dwarf that transits one member of the M+M binary system LHS 6343 AB every 12.71 days . The transits were discovered using photometric data from the Kelper public data release . The LHS 6343 stellar system was previously identified as a single high-proper-motion M dwarf . We use adaptive optics imaging to resolve the system into two low-mass stars with masses 0.370 \pm 0.009 M _ { \odot } and 0.30 \pm 0.01 M _ { \odot } , respectively , and a projected separation of 0 \farcs 55 . High-resolution spectroscopy shows that the more massive component undergoes Doppler variations consistent with Keplerian motion , with a period equal to the transit period and an amplitude consistent with a companion mass of M _ { C } = 62.9 \pm 2.3 M _ { Jup } . Based on our analysis of the transit light curve we estimate the radius of the companion to be R _ { C } = 0.833 \pm 0.021 R _ { Jup } , which is consistent with theoretical predictions of the radius of a > 1 Gyr brown dwarf .