  We provide important new constraints on the nature and redshift distribution
of optically faint (R>25) X-ray sources in the Chandra Deep Field South Survey.
We show that we can derive accurate photometric redshifts for the
spectroscopically unidentified sources thus maximizing the redshift
completeness for the whole X-ray sample. Our new redshift distribution for the
X-ray source population is in better agreement with that predicted by X-ray
background synthesis models; however, we still find an overdensity of low
redshift (z<1) sources. The optically faint sources are mainly X-ray absorbed
AGN, as determined from direct X-ray spectral analysis and other diagnostics.
Many of these optically faint sources have high (>10) X-ray-to-optical flux
ratios. We also find that ~71% of them are well fitted with the SED of an
early-type galaxy with <z_phot>~1.9 and the remaining 29% with irregular or
starburst galaxies mainly at z_phot>3. We estimate that 23% of the optically
faint sources are X-ray absorbed QSOs. The overall population of X-ray absorbed
QSOs contributes a ~15% fraction of the [2-10] keV X-ray Background (XRB)
whereas current XRB synthesis models predict a ~38% contribution.
