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 (Rapprox4kpc) 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.
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