  The next generation of telescopes aim to directly observe the first
generation of galaxies that initiated the reionization process in our Universe.
The Lyman Alpha (Lya) emission line is robustly predicted to be the most
prominent intrinsic spectral feature of these galaxies, making it an ideal
target to search for and study high redshift galaxies. Unfortunately the large
Gunn-Peterson optical depth of the surrounding neutral intergalactic medium
(IGM) is thought to render this line extremely difficult to detect prior to
reionization. In this paper we demonstrate that the radiative transfer effects
in the interstellar medium (ISM), which cause Lya flux to emerge from galaxies
at frequencies where the Gunn-Peterson optical depth is reduced, can
substantially enhance the prospects for detection of the Lya line at high
redshift. In particular, scattering off outflows of interstellar HI gas can
modify the Lya spectral line shape such that >5% of the emitted Lya radiation
is transmitted directly to the observer, even through a fully neutral IGM. It
may therefore be possible to directly observe `strong' Lya emission lines (EW >
50 Angstrom rest frame) from the highest redshift galaxies that reside in the
smallest HII `bubbles' early in the reionization era with JWST. In addition, we
show that outflows can boost the fraction of Lya radiation that is transmitted
through the IGM during the latter stages of reionization, and even
post-reionization. Coupled with the fact that the first generation of galaxies
are thought to have very large intrinsic equivalent Lya equivalent widths, our
results suggest that the search for galaxies in their redshifted Lya emission
line can be competitive with the drop-out technique out to the highest
redshifts that can be probed in the JWST era.
