We present results from two Chandra X-ray Observatory observations of the X-ray point source population in the nearby radio galaxy Centaurus A (NGC 5128). Using a wavelet decomposition detection algorithm, we detect 246 individual point sources above a limiting luminosity of ~2×1036 ergs s-1, 82 of which are detected in both data sets where the fields of view overlap. Thirty-eight sources were detected in only one observation but were within the field of view of both pointings, implying considerable variability. We identify eight foreground stars in our observations. We also identify nine of the sources with known globular clusters in Centaurus A. All previously observed ROSAT sources within our field of view are detected. The number of luminous (Lx>1037 ergs s-1) X-ray binaries per unit optical luminosity in Cen A is roughly consistent with that observed for the M31 bulge. There are approximately 50% more X-ray binaries per unit optical luminosity in Centaurus A than in the whole of M31, however. We find considerably fewer luminous X-ray binaries per unit optical luminosity in Cen A than in two other elliptical galaxies, M84 and NGC 4697, recently observed by Chandra. This result directly confirms the variance in the X-ray binary population with host galaxy optical luminosity previously inferred from spectral analysis of ROSAT and ASCA observations of elliptical galaxies.