We present deep narrow-band ( = 5390 A, = 77 A) 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 emission. Comparison with color-selected samples shows that the samples selected with these di erent 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 , and which are signi cant contributers to the integrated star formation at these epochs. For a Salpeter IMF we estimate a minimum star formation rate of 0.01M Mpc 3 yr 1 at z = 3:4 for H0 = 65 km s 1 Mpc 1 and q0 = 0.5 in the Ly -selected objects, though the value could be substantially higher if there is signi cant extinction. Subject headings: cosmology: early universe | cosmology: observations | galaxies: evolution | galaxies: formation Based in part on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. Visiting Astronomer, W. M. Keck Observatory, jointly operated by the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. Visiting Astronomer, Canada-France-Hawaii Telescope, operated by the National Research Council of Canada, the Centre National de la Recherche Scienti que of France, and the University of Hawaii.