  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and optical spectra for 25, including 5 previously unpublished redshifts.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.
