  We present results from a spectral analysis of a sample of high-redshift
(z>3) X-ray selected AGN in the 4 Ms Chandra Deep Field South (CDF-S), the
deepest X-ray survey to date. The sample is selected using the most recent
spectroscopic and photometric information available in this field. It consists
of 34 sources with median redshift z=3.7, 80 median net counts in the 0.5-7 keV
band and median rest-frame absorption-corrected luminosity $L_{2-10
\rmn{keV}}\approx1.5\times10^{44}\rmn{erg} \rmn{s^{-1}}$. Spectral analysis for
the full sample is presented and the intrinsic column density distribution,
corrected for observational biases using spectral simulations, is compared with
the expectations of X-ray background (XRB) synthesis models. We find that
$\approx57$ per cent of the sources are highly obscured
($N_H>10^{23}\rmn{cm^{-2}}$). Source number counts in the $0.5-2\rmn{keV}$ band
down to flux $F_{0.5-2 \rmn{keV}}\approx4\times10^{-17}\rmn{erg}
\rmn{s^{-1}cm^{-2}}$ are also presented. Our results are consistent with a
decline of the AGN space density at z>3 and suggest that, at those redshifts,
the AGN obscured fraction is in agreement with the expectations of XRB
synthesis models.
