  This study presents the final source catalog of the Chandra ACIS Survey of
M33 (ChASeM33). With a total exposure time of 1.4 Ms, ChASeM33 covers ~70% of
the D25 isophote (R\approx4kpc) of M33 and provides the deepest, most complete,
and detailed look at a spiral galaxy in X-rays. The source catalog includes 662
sources, reaches a limiting unabsorbed luminosity of ~2.4x10^(34) erg/s in the
0.35-8.0keV energy band, and contains source positions, source net counts,
fluxes and significances in several energy bands, and information on source
variability. The analysis challenges posed by ChASeM33 and the techniques
adopted to address these challenges are discussed. To constrain the nature of
the detected X-ray source, hardness ratios were constructed and spectra were
fit for 254 sources, followup MMT spectra of 116 sources were acquired, and
cross-correlations with previous X-ray catalogs and other multi-wavelength data
were generated. Based on this effort, 183 of the 662 ChASeM33 sources could be
identified. Finally, the luminosity function for the detected point sources as
well as the one for the X-ray binaries in M33 is presented. The luminosity
functions in the soft band (0.5-2.0 keV) and the hard band (2.0-8.0 keV) have a
limiting luminosity at the 90% completeness limit of 4.0x10^(34) erg/s and
1.6x10^(35) erg/s (for D=817kpc), respectively, which is significantly lower
than what was reported by previous X-ray binary population studies in galaxies
more distant than M33. The resulting distribution is consistent with a dominant
population of high mass X-ray binaries as would be expected for M33.
