  We report the serendipitous detection in high-resolution optical spectroscopy
of a strong, asymmetric Ly-alpha emission line at z = 5.190. The detection was
made in a 2.25 hour exposure with the Echelle Spectrograph and Imager on the
Keck II telescope through a spectroscopic slit of dimensions 1" x 20". The
progenitor of the emission line, J123649.2+621539 (hereafter ES1), lies in the
Hubble Deep Field North West Flanking Field where it appears faint and compact,
subtending just 0.3" (FWHM) with I(AB) = 25.4. The ES1 Ly-alpha line flux of
3.0 x 10^(-17) ergs/cm^2/s corresponds to a luminosity of 9.0 x 10^(42) ergs/s,
and the line profile shows the sharp blue cut-off and broad red wing commonly
observed in star-forming systems and expected for radiative transfer in an
expanding envelope. We find that the Ly-alpha profile is consistent with a
galaxy-scale outflow with a velocity of v > 300 km/s. This value is consistent
with wind speeds observed in powerful local starbursts (typically 10^2 to 10^3
km/s), and compares favorably to simulations of the late-stage evolution of
Ly-alpha emission in star-forming systems. We discuss the implications of this
high-redshift galactic wind for the early history of the evolution of galaxies
and the intergalactic medium, and for the origin of the UV background at z > 3.
