  We present an analysis of the compact X-ray source population in the
Seyfert~2 galaxy NGC 1068, imaged with Chandra. We find a total of 84 compact
sources, of which 66 are projected onto the galactic disk of NGC 1068. Spectra
of the brightest sources have been modeled with both multi-color disk blackbody
and power-law models. The power-law model provides the better description of
the spectrum for most of these sources. Five sources have 0.4-8 keV intrinsic
luminosities greater than 10^{39} erg/s, assuming that their emission is
isotropic and that they are associated with NGC 1068. We refer to these sources
as Intermediate Luminosity X-ray Objects (IXOs). If these five sources are
X-ray binaries accreting with luminosities that are both sub-Eddington and
isotropic, then the implied source masses are >7 solar masses, and so they are
inferred to be black holes. The brightest source has a much harder spectrum
(Gamma = 0.9\pm0.1) than that found in Galactic black hole candidates and other
IXOs. It also shows large-amplitude variability on both short-term and
long-term timescales. The ratio of the number of sources with luminosities
greater than 2.1 x 10^{38} erg/s in the 0.4-8 keV band to the rate of massive
star formation is the same, to within a factor of two, for NGC 1068, the
Antennae, NGC 5194 (the main galaxy in M51), and the Circinus galaxy. This
suggests that the rate of production of X-ray binaries per massive star is
approximately the same for galaxies with currently active star formation,
including ``starbursts''.
