The discovery of a few truly primordial galaxies -- that is, chemically primitive systems undergoing their first generation of star formation -- will be a key step in our efforts to understand how galaxies form and evolve. The Large Area Lyman Alpha survey is an ongoing effort to identify a large sample of young galaxies at high redshifts (z=4.5 and z=5.7) using the strong Lyman alpha emission line expected in such objects. We have achieved sensitivity comparable to the deepest published surveys (~2e-17 erg/cm2/s) over a volume many times larger (~1e6 comoving Mpc^3). Spectroscopic followup of our sample confirms a substantial population of faint, high redshift Lyman alpha emitting galaxies. Many of these objects have extremely large equivalent widths, which imply some combination of extreme youth, very low metallicity, and an initial mass function dominated by high mass stars. The presence of Lyman alpha galaxies at high redshift allows a robust test of the reionization epoch completely independent of the Gunn-Peterson effect. We have applied this test to show that reionization was earlier than z=5.7. Future extensions of this work using both NOAO telescopes and the NASA Great Observatories will allow us to study the physical nature of these galaxies in more detail and to find them at higher redshifts and fainter flux levels.