We report the discovery of a substantial population of star–forming galaxies at . These galaxies have been selected using color criteria sensitive to the presence of a Lyman continuum break superposed on an otherwise very blue far-UV continuum, and then confirmed with deep spectroscopy on the W. M. Keck telescope. The surface density of galaxies brighter than R=25 with 3 < z < 3.5 is galaxies arcmin, approximately 1.3% of the deep counts at these magnitudes; this value applies both to ``random’’ fields and to fields centered on known QSOs. The corresponding co-moving space density is approximately half that of luminous () present–day galaxies. Our sample of galaxies is large enough that we can begin to detail the spectroscopic characteristics of the population as a whole. The spectra of the galaxies are remarkably similar to those of nearby star-forming galaxies, the dominant features being strong low–ionization interstellar absorption lines and high–ionization stellar lines, often with P-Cygni profiles characteristic of Wolf-Rayet and O–star winds. Lyman emission is generally weak ( \AA\ rest equivalent width) and is absent for >50% of the galaxies. The star formation rates, measured directly from the far-UV continua, lie in the range 4-25 M yr for . Together with the morphological properties of the galaxy population, which we discuss in a companion paper (Giavalisco \et 1996), all of these findings strongly suggest that we have identified the high-redshift counterparts of the spheroid component of present–day luminous galaxies. In any case, it is clear that massive galaxy formation was already well underway by . (shortened abstract). arch-ive/yymmnnn

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