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{Abridged} We report the discovery of six compact, starburst galaxycandidates with redshifts 2.3 < z < 2.8 and r-band magnitudes 19.8-20.5 in theQuasar Catalog of the Sloan Digital Sky Survey First Data Release (SDSS DR1).The SDSS spectra of these objects resemble the composite spectrum of LymanBreak Galaxies (LBGs) at z ~ 3 (albeit with some differences and broaderspectral lines), but the systems are 4-5 magnitudes brighter than an ``L*'' LBGand 2-3 magnitudes brighter than the most luminous objects in typical LBGspectroscopic surveys. These objects could be extremely luminous LBGs, normalLBGs amplified by gravitational lensing (like MS 1512-cB58), or a rare class ofunusual BAL quasars. Under the first hypothesis, star formation rates inferredfrom the UV continuum luminosities are about 300-1000 M_sun yr^-1 with nocorrection for dust extinction. The SDSS images show no evidence of multipleimaging or foreground lensing structures, but lensing amplification cannot beruled out with the present data. The spectra have fairly broad absorptionfeatures and prominent high-ionization absorption, but they do not have highionization emission lines, nor do they resemble spectra of known BAL quasars.Assuming that lensing and AGN contributions are unimportant, we estimate thehigh end of the z ~ 2.5 galaxy luminosity function, making the crude butconservative assumption of unit detection efficiency over our observed redshiftand magnitude range. The estimated comoving space density is above a Schechterfunction extrapolation of the LBG luminosity function from fainter magnitudes.Improved optical spectra and measurements at X-ray, IR, and sub-mm wavelengthscould help determine the nature of these remarkable objects.Comment: 12 pages, 2 tables, 2 figures, submitted to ApJ Letters; replaced  figure 1 and revised text in response to comments on the original version;  final refereed versio

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