We report on the properties of a sample of ultraviolet luminous galaxies (UVLGs) selected by matching the Galaxy Evolution Explorer (GALEX) All-sky Imaging and Medium Imaging Surveys with the Sloan Digital Sky Survey Third Data Release. The overlap between these two surveys is roughly 450 square degrees. Out of 25362 galaxies (with SDSS spectroscopy) between 0.0 < z < 0.3 detected by GALEX, there are 215 galaxies with L > 2 × 10 L⊙ at 1530 Å (observed wavelength). The properties of this population are well correlated with ultraviolet surface brightness. We find that the galaxies with low UV surface brightness are primarily large spiral systems with a mixture of old and young stellar populations, while the high surface brightness galaxies consist primarily of compact starburst systems, with an approximate boundary at a surface brightness of I1530 = 10 8 L⊙ kpc . The large galaxies appear to be the high-luminosity tail of the galaxy star formation function, and owe their large luminosity to their large surface area. In terms of the behavior of surface brightness with luminosity, size with luminosity, the mass-metallicity relation, and other parameters, the compact UVLGs clearly depart from the trends established by the full sample of galaxies. The subset of compact UVLGs with the highest surface brightness (I1530 > 10 9 L⊙ kpc ; “supercompact UVLGs”) have characteristics that are remarkably similar to Lyman Break Galaxies at higher redshift. They are much more luminous (and thus have much higher star formation rates) than typical local ultraviolet-bright starburst galaxies and blue compact dwarf galaxies. They have metallicities that are systematically lower than normal galaxies of the same stellar mass, indicating that they are less chemically evolved. In all these respects, they are the best local analogs for Lyman Break Galaxies. Department of Physics and Astronomy, The Johns Hopkins University, Homewood Campus, Baltimore, MD 21218 Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 California Institute of Technology, MC 405-47, 1200 East California Boulevard, Pasadena, CA 91125 Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721 Department of Astronomy, Columbia University, New York, NY 10027 Max-Planck-Institut fur Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching bei Munchen, Germany Institut d’Astrophysique de Paris, UMR 7095, 98 bis Boulevard Arago, F-75014 Paris, France Laboratory for Astronomy and Solar Physics, NASA Goddard Space Flight Center, Greenbelt, MD 20771 Laboratoire d’Astrophysique de Marseille, BP 8, Traverse du Siphon, 13376 Marseille Cedex 12, France Center for Space Astrophysics, Yonsei University, Seoul 120-749, Korea Observatories of the Carnegie Institution of Washington, 813 Santa Barbara St., Pasadena, CA 91101 Space Sciences Laboratory, University of California at Berkeley, 601 Campbell Hall, Berkeley, CA 94720