  We report the first unambiguous detection and mass measurement of an isolated
stellar-mass black hole (BH). We used the Hubble Space Telescope (HST) to carry
out precise astrometry of the source star of the long-duration (t_E~270 days),
high-magnification microlensing event MOA-2011-BLG-191/OGLE-2011-BLG-0462
(hereafter designated as MOA-11-191/OGLE-11-462), in the direction of the
Galactic bulge. HST imaging, conducted at eight epochs over an interval of six
years, reveals a clear relativistic astrometric deflection of the background
star's apparent position. Ground-based photometry of MOA-11-191/OGLE-11-462
shows a parallactic signature of the effect of the Earth's motion on the
microlensing light curve. Combining the HST astrometry with the ground-based
light curve and the derived parallax, we obtain a lens mass of 7.1 +/- 1.3 Msun
and a distance of 1.58 +/- 0.18 kpc. We show that the lens emits no detectable
light, which, along with having a mass higher than is possible for a white
dwarf or neutron star, confirms its BH nature. Our analysis also provides an
absolute proper motion for the BH. The proper motion is offset from the mean
motion of Galactic-disk stars at similar distances by an amount corresponding
to a transverse space velocity of ~45 km/s, suggesting that the BH received a
'natal kick' from its supernova explosion. Previous mass determinations for
stellar-mass BHs have come from radial-velocity measurements of Galactic X-ray
binaries, and from gravitational radiation emitted by merging BHs in binary
systems in external galaxies. Our mass measurement is the first for an isolated
stellar-mass BH using any technique.
