Long-duration Gamma-Ray Bursts (GRBs) allow us to pinpoint and study star-forming galaxies in the early universe, thanks to their orders of magnitude brighter peak luminosities compared to other astrophysical sources, and their association with deaths of massive stars. We present Hubble Space Telescope Wide Field Camera 3 detections of three Swift GRB host galaxies lying at redshifts $z = 5.913$ (GRB 130606A), $z = 6.295$ (GRB 050904), and $z = 6.327$ (GRB 140515A) in the F140W (wide-$JH$ band, $lambda_{rm{obs}}sim1.4,mu m$) filter. The hosts have magnitudes (corrected for Galactic extinction) of $m_{rm{lambda_{obs},AB}}= 26.34^{+0.14}_{-0.16}, 27.56^{+0.18}_{-0.22},$ and $28.30^{+0.25}_{-0.33}$ respectively. In all three cases the probability of chance coincidence of lower redshift galaxies is $lesssim2,%$, indicating that the detected galaxies are most likely the GRB hosts. These are the first detections of high redshift ($z > 5$) GRB host galaxies in emission. The galaxies have luminosities in the range $0.1-0.6,L^{*}_{z=6}$ (with $M_{1600}^{*}=-20.95pm0.12$), and half-light radii in the range $0.6-0.9,rm{kpc}$. Both their half-light radii and luminosities are consistent with existing samples of Lyman-break galaxies at $zsim6$. Spectroscopic analysis of the GRB afterglows indicate low metallicities ($[rm{M/H}]lesssim-1$) and low dust extinction ($A_{rm{V}}lesssim0.1$) along the line of sight. Using stellar population synthesis models, we explore the implications of each galaxys luminosity for its possible star formation history, and consider the potential for emission-line metallicity determination with the upcoming James Webb Space Telescope.
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