  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
CFHT/WIRCam photocenter astrometry and Keck adaptive optics resolved imaging,
we measure the first high-quality parallactic distance ($6.80_{-0.06}^{+0.05}$
pc) and orbit ($8.06_{-0.25}^{+0.24}$ yr period) for this system composed of a
low-mass star and brown dwarf. We find a moderately eccentric orbit ($e =
0.240_{-0.010}^{+0.009}$), incompatible with previous work based on less data,
and dynamical masses of $99\pm6$ $M_{\rm Jup}$ and $66\pm4$ $M_{\rm Jup}$ for
the two components. The primary mass is marginally inconsistent (2.1$\sigma$)
with the empirical mass$-$magnitude$-$metallicity relation and models of
main-sequence stars. The relatively high mass of the cold ($T_{\rm eff} =
1250\pm40$ K) brown dwarf companion indicates an age older than a few Gyr, in
accord with age estimates for the primary star, and is consistent with our
recent estimate of $\approx$70 $M_{\rm Jup}$ 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 $68.7\pm2.0$ kAU of the Sun $80.5\pm0.7$ kyr ago,
passing through the outer Oort cloud where comets can have stable orbits.
