We present the main results from our 940 ksec observation of the Chandra Deep Field South ( CDFS ) , using the source catalog described in an accompanying paper ( Giacconi et al . 2001 ) . We extend the measurement of source number counts to 5.5 \times 10 ^ { -17 } \hbox { erg cm$ { } ^ { -2 } $ s$ { } ^ { -1 } $ } in the soft 0.5–2 keV band and 4.5 \times 10 ^ { -16 } \hbox { erg cm$ { } ^ { -2 } $ s$ { } ^ { -1 } $ } in the hard 2–10 keV band . The hard band Log N–Log S shows a significant flattening ( slope \simeq 0.6 ) below \approx 10 ^ { -14 } \hbox { erg cm$ { } ^ { -2 } $ s$ { } ^ { -1 } $ } , leaving at most 10–15 % of the X–ray background ( XRB ) to be resolved , the main uncertainty lying in the measurement of the total flux of the XRB . On the other hand , the analysis in the very hard 5–10 keV band reveals a relatively steep Log N–Log S ( slope \simeq 1.3 ) down to 10 ^ { -15 } \hbox { erg cm$ { } ^ { -2 } $ s$ { } ^ { -1 } $ } . Together with the evidence of a progressive flattening of the average X–ray spectrum near the flux limit , this indicates that there is still a non negligible population of faint hard sources to be discovered at energies not well probed by Chandra , which possibly contribute to the 30 keV bump in the spectrum of the XRB . We use optical redshifts and identifications , obtained with the VLT , for one quarter of the sample to characterize the combined optical and X–ray properties of the CDFS sample . Different source types are well separated in a parameter space which includes X–ray luminosity , hardness ratio and R - K color . Type II objects , while redder on average than the field population , have colors which are consistent with being hosted by a range of galaxy types . Type II AGN are mostly found at z \lesssim 1 , in contrast with predictions based on AGN population synthesis models , thus suggesting a revision of their evolutionary parameters .