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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.