Bright Lyman Break Galaxy Candidates in the Sloan Digital Sky Survey First Data Release

{Abridged} We report the discovery of six compact, starburst galaxy candidates with redshifts 2.3 < z < 2.8 and r-band magnitudes 19.8-20.5 in the Quasar Catalog of the Sloan Digital Sky Survey First Data Release (SDSS DR1). The SDSS spectra of these objects resemble the composite spectrum of Lyman Break Galaxies (LBGs) at z ~ 3 (albeit with some differences and broader spectral lines), but the systems are 4-5 magnitudes brighter than an ``L*'' LBG and 2-3 magnitudes brighter than the most luminous objects in typical LBG spectroscopic surveys. These objects could be extremely luminous LBGs, normal LBGs amplified by gravitational lensing (like MS 1512-cB58), or a rare class of unusual BAL quasars. Under the first hypothesis, star formation rates inferred from the UV continuum luminosities are about 300-1000 M_sun yr^-1 with no correction for dust extinction. The SDSS images show no evidence of multiple imaging or foreground lensing structures, but lensing amplification cannot be ruled out with the present data. The spectra have fairly broad absorption features and prominent high-ionization absorption, but they do not have high ionization emission lines, nor do they resemble spectra of known BAL quasars. Assuming that lensing and AGN contributions are unimportant, we estimate the high end of the z ~ 2.5 galaxy luminosity function, making the crude but conservative assumption of unit detection efficiency over our observed redshift and magnitude range. The estimated comoving space density is above a Schechter function extrapolation of the LBG luminosity function from fainter magnitudes. Improved optical spectra and measurements at X-ray, IR, and sub-mm wavelengths could help determine the nature of these remarkable objects.