We report observations of the recently discovered, nearby late-M dwarf WISE J072003.20-084651.2. New astrometric measurements obtained with the TRAPPIST telescope improve the distance measurement to 6.0 ± 1.0 pc and confirm the low tangential velocity (3.5 ± 0.6 km s −1 ) reported by Scholz. Low-resolution optical spectroscopy indicates a spectral type of M9.5 and prominent Hα emission (á ñ a L L log H 10 bol = −4.68 ± 0.06), but no evidence of subsolar metallicity or Li I absorption. Near-infrared spectroscopy reveals subtle peculiarities that can be explained by the presence of a T5 binary companion, and high-resolution laser guide star adaptive optics imaging reveals a faint (ΔH = 4.1) candidate source 0. 14 (0.8 AU) from the primary. With high-resolution optical and near-infrared spectroscopy, we measure a stable radial velocity of +83.8 ± 0.3 km s −1 , indicative of old disk kinematics and consistent with the angular separation of the possible companion. We measure a projected rotational velocity of v sin i = 8.0 ± 0.5 km s −1 and find evidence of low-level variabilty (∼1.5%) in a 13 day TRAPPIST light curve, but cannot robustly constrain the rotational period. We also observe episodic changes in brightness (1%-2%) and occasional flare bursts (4%-8%) with a 0.8% duty cycle, and order-of-magnitude variations in Hα line strength. Combined, these observations reveal WISE J0720-0846 to be an old, very low-mass binary whose components straddle the hydrogen burning minimum mass, and whose primary is a relatively rapid rotator and magnetically active. It is one of only two known binaries among late M dwarfs within 10 pc of the Sun, both of which harbor a mid T-type brown dwarf companion. We show that while this specific configuration is rare (≲1.6% probability), roughly 25% of binary companions to late-type M dwarfs in the local population are likely low-temperature T or Y brown dwarfs.