[en] 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 ± 0.017 days. Its velocity semi-amplitude of 21.4 ± 0.5 km s^–1 corresponds to a minimum mass of 61 ± 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 yr) 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.''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 ± 0.08 pc) and the only among these with all M-dwarf (or cooler) components.