  In the course of our ongoing search for serendipitous high-redshift Lyman
alpha (LyA) Emissionin deep archival Keck spectra, we discovered two very high
equivalent width (W_{obs} ~ 450A, 2-sigma) LyA emission line candidates at z ~3
in a moderate dispersion (R~1200) spectrogram. Both lines have low velocity
dispersions (sigma_v ~ 60 km/s) and deconvolved radii r ~ 1 kpc (h = 0.5). We
argue that the lines are LyA, and are powered by stellar ionization. The
surface density of robust, high equivalent width LyA candidates is estimated to
be ~3 \pm 2 per arcmin^2 per unit redshift at z ~ 3, consistent with the
estimate of Cowie etal (1998). The LyA emission line source characteristics are
consistent with the galaxies undergoing their first burst of star formation,
ie, with being primeval. Source sizes and velocity dispersions are comparable
to the theoretical primeval galaxy model of Lin and Murray (1992) based on the
inside-out, self-similar collapse of an isothermal sphere. In this model, star
formation among field galaxies is a protracted process. Galaxies are thought to
be able to display high equivalent widths for only the first few x 10 Myr. This
time is short in relation to the difference in look back times between z=3 and
z=4, and implies that a substantial fraction of strong line-emitting galaxies
at z=3 were formed at redshifts z < 4. We discuss the significance of
high-equivalent width LyA-emitting galaxies in terms of the emerging picture of
the environment, and the specific characteristics of primeval galaxy formation
at high redshift.
