  We identify 233 X-ray sources, of which 95 are new, in a 222 ks exposure of
Omega Centauri with the Chandra X-ray Observatory's ACIS-I detector. The
limiting unabsorbed flux in the core is $f_x$ (0.5$-$6.0 keV) $\simeq$ 3
$\times$ 10$^{-16}$ erg s$^{-1}$ cm$^{-2}$ ($L_X$ $\simeq$ 1 $\times$ 10$^{30}$
erg s$^{-1}$ at 5.2 kpc). We estimate that ~$60\pm 20$ of these are cluster
members, of which ~30 lie within the core ($r_c$ $=$ 155 arcsec), and another
~30 between 1$-$2 core radii. We identify four new optical counterparts, for a
total of 45 likely identifications. Probable cluster members include 18
cataclysmic variables (CVs) and CV candidates, one quiescent low-mass X-ray
binary, four variable stars, and five stars that are either associated with w
Cen's anomalous red giant branch, or are sub-subgiants. We estimate that the
cluster contains $40\pm 10$ CVs with $L_X$ $>$ 10$^{31}$ erg s$^{-1}$,
confirming that CVs are underabundant in w Cen relative to the field. Intrinsic
absorption is required to fit X-ray spectra of six of the nine brightest CVs,
suggesting magnetic CVs, or high-inclination systems. Though no radio
millisecond pulsars (MSPs) are currently known in w Cen, more than 30
unidentified sources have luminosities and X-ray colours like those of MSPs
found in other globular clusters; these could be responsible for the
Fermi-detected gamma-ray emission from the cluster. Finally, we identify a CH
star as the counterpart to the second-brightest X-ray source in the cluster and
argue that it is a symbiotic star. This is the first such giant/white dwarf
binary to be identified in a globular cluster.
