  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 $M_{1600}^{*}=-20.95\pm0.12$), 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 $z\sim6$. 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 galaxy's luminosity for
its possible star formation history, and consider the potential for
emission-line metallicity determination with the upcoming James Webb Space
Telescope.
