  (abridged) We present a catalog of 2357 point sources detected during 590 ks
of Chandra observations of the 17-by-17 arcminute field around Sgr A*. This
field encompasses a physical area of 40 by 40 pc at a distance of 8 kpc. The
completeness limit of the sample at the Galactic center is 10^{31} erg s^{-1}
(2.0--8.0 keV), while the detection limit is an order of magnitude lower. The
281 sources detected below 1.5 keV are mainly in the foreground of the Galactic
center, while comparisons to the Chandra deep fields at high Galactic latitudes
suggest that only about 100 of the observed sources are background AGN. The
surface density of absorbed sources (not detected below 1.5 keV) falls off as
1/theta away from Sgr A*, in agreement with the distribution of stars in
infrared surveys. Point sources brighter than our completeness limit produce
10% of the flux previously attributed to diffuse emission. The log(N)-log(S)
distribution of the Galactic center sources is extremely steep (power-law slope
alpha = 1.7). If this distribution extends down to a flux of 10^{-17} erg
cm^{-1} s^{-1} (10^{29} erg s^{-1} at 8 kpc, 2.0--8.0 keV) with the same slope,
then point sources would account for all of the previously reported diffuse
emission. Therefore, the 2.0--8.0 keV luminosity distribution must flatten
between 10^{29} - 10^{31} erg s^{-1}. Finally, the spectra of more than half of
the Galactic center sources are very hard, and can be described by a power law
($E^{-Gamma}) with photon index Gamma < 1. Such hard spectra have been seen
previously only from magnetically accreting white dwarfs and wind-accreting
neutron stars, suggesting that there are large numbers of these systems in our
field.
