We present individual dynamical masses for the nearby M9.5+T5.5 binary WISE J072003.20−084651.2AB, a.k.a. Scholz's star. Combining high-precision Canada–France–Hawaii Telescope/WIRCam photocenter astrometry and Keck adaptive optics resolved imaging, we measure the first high-quality parallactic distance (6.80^(+0.05)_(−0.06) pc) and orbit (8.06^(+0.24)_(−0.25) yr period) for this system composed of a low-mass star and brown dwarf. We find a moderately eccentric orbit (e = 0.240^(+0.009)_(−0.010)), incompatible with previous work based on less data, and dynamical masses of 99 ± 6 M_(Jup) and 66 ± 4 M_(Jup) for the two components. The primary mass is marginally inconsistent (2.1σ) with the empirical mass–magnitude–metallicity relation and models of main-sequence stars. The relatively high mass of the cold (T_(eff) = 1250±40 K) brown dwarf companion indicates an age older than a few gigayears, in accord with age estimates for the primary star, and is consistent with our recent estimate of ≈70 M_(Jup) for the stellar/substellar boundary among the field population. Our improved parallax and proper motion, as well as an orbit-corrected system velocity, improve the accuracy of the system's close encounter with the solar system by an order of magnitude. WISE J0720−0846AB passed within 68.7 ± 2.0 kau of the Sun 80.5 ± 0.7 kyr ago, passing through the outer Oort cloud where comets can have stable orbits.