  The origin of the X-ray background, in particular at hard (2-10 keV)
energies, has been a debated issue for more than 30 years. The Chandra deep
fields provide the deepest look at the X-ray sky and are the best dataset to
study the X-ray background. We searched the Chandra Deep Field South for X-ray
sources with the aid of a dedicated wavelet-based algorithm. We are able to
reconstruct the Log N-Log S source distribution in the soft (0.5-2 keV) and
hard (2-10 keV) bands down to limiting fluxes of 2x10^{-17} erg s^{-1} cm^{-2}
and 2x10^{-16} erg s^{-1} cm^{-2}, respectively. These are a factor ~5 deeper
than previous investigations. We find that the soft relation continues along
the extrapolation from higher fluxes, almost completely accounting for the soft
X-ray background. On the contrary, the hard distribution shows a flattening
below ~2x10^{-14} erg s^{-1} cm^{-2}. Nevertheless, we can account for >68% of
the hard X-ray background, with the main uncertainty being the sky flux itself.
