We report new infrared radial velocity measurements obtained with CSHELL at NASA ’ s Infrared Telescope Facility that reveal the M3.5 dwarf GJ 867B to be a single-lined spectroscopic binary with a period of 1.795 \pm 0.017 days . Its velocity semi-amplitude of 21.4 \pm 0.5 kms ^ { -1 } corresponds to a minimum mass of 61 \pm 7 M _ { JUP } ; the new companion , which we call GJ 867D , could be a brown dwarf . Stable astrometric measurements of GJ 867BD obtained with CTIO ’ s 0.9-m telescope over the last decade exclude the presence of any massive planetary companions ( 7-18 M _ { JUP } ) with longer orbital periods ( 2-10 years ) for the majority of orientations . These complementary observations are also used to determine the trigonometric distance and proper motion of GJ 867BD ; the measurements are consistent with the HIPPARCOS measured values of the M2 dwarf GJ 867AC , which is itself a 4.1 day double-lined spectroscopic binary at a projected separation of 24 \farcs 5 ( 216 AU ) from GJ 867BD . These new measurements strengthen the case that GJ 867AC and GJ 867BD are physically associated , making the GJ 867 system one of only four quadruple systems within 10 pc of the Sun ( d = 8.82 \pm 0.08 pc ) and the only among these with all M-dwarf ( or cooler ) components .