  We use Chandra deep observations of the Galactic Center (GC) region to
improve the constraints on the unresolved fraction of the Galactic X-ray
background (also known as the Galactic ridge X-ray emission). We emphasize the
importance of correcting the measured source counts at low fluxes for bias
associated with Poisson noise. We find that at distances of 2'-4' from Sgr A*
at least ~40% of the total X-ray emission in the energy band 4-8 keV originates
from point sources with luminosities L(2-10 keV)> 10^{31} erg/sec. From a
comparison of the source number-flux function in the GC region with the known
luminosity function of faint X-ray sources in the Solar vicinity, we infer that
Chandra has already resolved a large fraction of the cumulative contribution of
cataclysmic variables to the total X-ray flux from the GC region. This
comparison further indicates that most of the yet unresolved ~60% of the X-ray
flux from the GC region is likely produced by weak cataclysmic variables and
coronally active stars with L(2-10 keV)<10^{31} erg/sec. We conclude that the
bulk of the Galactic X-ray background is produced by discrete sources.
