  We report the discovery of Tucana B, an isolated ultra-faint dwarf galaxy at
a distance of D=1.4 Mpc. Tucana B was found during a search for ultra-faint
satellite companions to the known dwarfs in the outskirts of the Local Group,
although its sky position and distance indicate the nearest galaxy to be
$\sim$500 kpc distant. Deep ground-based imaging resolves Tucana B into stars,
and it displays a sparse red giant branch consistent with an old, metal poor
stellar population analogous to that seen in the ultra-faint dwarf galaxies of
the Milky Way, albeit at fainter apparent magnitudes. Tucana B has a half-light
radius of 80$\pm$40 pc, and an absolute magnitude of
$M_V$=$-$6.9$^{+0.5}_{-0.6}$ mag ($L_V$=$(5^{+4}_{-2})\times$10$^4$
$L_{\odot}$), which is again comparable to the Milky Way's ultra-faint
satellites. There is no evidence for a population of young stars, either in the
optical color magnitude diagram or in GALEX archival ultraviolet imaging, with
the GALEX data indicating $\log (\mathrm{SFR_{NUV}/M_\odot \, yr^{-1}}) < -5.4$
for star formation on $\lesssim$100 Myr time scales. Given its isolation and
physical properties, Tucana B may be a definitive example of an ultra-faint
dwarf that has been quenched by reionization, providing strong confirmation of
a key driver of galaxy formation and evolution at the lowest mass scales. It
also signals a new era of ultra-faint dwarf galaxy discovery at the extreme
edges of the Local Group.
