We have analyzed optically bright, X-ray faint [OBXF; i.e., log(fX/fR) < -2] sources identified in an 178.9 square arcminute area within the Chandra Deep Field-North (CDF-N) 2 Ms survey. We find 43 OBXF sources in this area, comprising ~15% of the X-ray sources above a 0.5--2 keV flux of 2.3e-17 erg cm^-2 s^-1. We present spectroscopic identifications for 42 of the OBXF sources and optical spectra for 25, including 5 previously unpublished redshifts. Deep optical imaging data (either HST or ground-based) are presented for all the OBXF sources. The OBXF population consists mainly of normal and starburst galaxies detected out to cosmologically significant distances (i.e., to a median redshift of z=0.297 and a full redshift range z=0.06-0.845). This is notable since these distances equate to look-back times of up to ~8 Gyr; we are thus provided with a window on the X-ray emission from galaxies at redshifts much closer to the cosmic star formation peak than was possible prior to Chandra. The X-ray luminosity distribution of OBXF sources extends to higher luminosity than does that of normal galaxies indicating that a significant fraction are likely dominated by low-luminosity AGN (LLAGN) or vigorous star formation. By combining the detected X-ray counts, we find the average OBXF X-ray spectrum to be consistent with a Gamma=2.0 power law. The 0.5--2 keV log N-log S for the OBXF galaxies is much steeper (alpha=-1.7) than for the general X-ray source population. Indeed, the number of OBXF sources has doubled between the 1~Ms and 2~Ms survey, rising sharply in numbers at faint fluxes. The extragalactic OBXF sources are found to contribute ~1-2% of the soft extragalactic X-ray background.
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