We present an analysis of the compact X-ray source population in the Seyfert 2 galaxy NGC 1068, imaged with a ~50 ks Chandra observation. We find a total of 84 compact sources on the S3 chip, of which 66 are located within the 25.0 B-mag arcsec^-2 isophote of the galactic disk of NGC 1068. Spectra have been obtained for the 21 sources with at least 50 counts and modeled with both multicolor disk blackbody and power-law models. The power-law model provides the better description of the spectrum for 18 of these sources. For fainter sources, the spectral index has been estimated from the hardness ratio. Five sources have 0.4-8 keV intrinsic luminosities greater than 10³⁹ ergs s^-1, 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 M, and so they are inferred to be black holes. Most of the spectrally modeled sources have spectral shapes similar to Galactic black hole candidates. However, the brightest compact source in NGC 1068 has a spectrum that is much harder than that found in Galactic black hole candidates and other IXOs. The brightest source also shows large amplitude variability on both short-term and long-term timescales, with the count rate possibly decreasing by a factor of 2 in ~2 ks during our Chandra observation, and the source flux decreasing by a factor of 5 between our observation and the grating observations taken just over 9 months later. The ratio of the number of sources with luminosities greater than 2.1 × 10³⁸ ergs s^-1 in the 0.4-8 keV band to the rate of massive (>5 M) star formation is the same, to within a factor of 2, 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."