  We present deep narrow-band (lambda = 5390 Angstroms, delta lambda = 77
Angstroms) and multi-color observations of the Hubble Deep Field and the Hawaii
Deep Field SSA22 obtained with the LRIS instrument at the Keck II 10-m
telescope. It is shown that there is a substantial population of galaxies at
z~3.4 which can be selected by Ly alpha emission. Comparison with
color-selected samples shows that the samples selected with these different
criteria have substantial, but not complete overlap, and that there is a
comparable surface density in the two selected populations. The emission-line
selected samples include objects with strong Ly alpha, and which are
significant contributers to the integrated star formation at these epochs. For
a Salpeter IMF we estimate a minimum star formation rate of 0.01 solar masses
per cubic Mpc per yr at z=3.4 for H_0 = 65 km/s/Mpc and q_0 = 0.5 in the Ly
alpha-selected objects, though the value could be substantially higher if there
is significant extinction.
