M33 contains a large number of emission nebulae identified as supernova remnants (SNRs) based on the high [S II]:Ha ratios characteristic of shocked gas. Using Chandra data from the ChASeM33 survey with a 0.35-2 keV sensitivity of about 2 x 10**34 ergs/s, we have detected 82 of 137 SNR candidates, yielding confirmation of (or at least strongly support for) their SNR identifications. This provides the largest sample of remnants detected at optical and X-ray wavelengths in any galaxy, including the Milky Way. A spectral analysis of the seven X-ray brightest SNRs reveals that two, G98-31 and G98-35, have spectra that appear to indicate enrichment by ejecta from core-collapse supernova explosions. In general, the X-ray detected SNRs have soft X-ray spectra compared to the vast majority of sources detected along the line of sight to M33. It is unlikely that there are any other undiscovered thermally dominated X-ray SNRs with luminosities in excess of about 4 x 10**35 ergs/s in the portions of M33 covered by the ChASeM33 survey. We have used a combination of new and archival optical and radio observations to attempt to better understand why some objects are detected as X-ray sources and others are not. We have also developed a morphological classification scheme for the optically-identified SNRs, and discuss the efficacy of this scheme as a predictor of X-ray detectability. Finally, we have compared the SNRs found in M33 to those that have been observed in the Galaxy and the Magellanic Clouds. There are no close analogs of Cas A, Keplers SNR, Tychos SNR or the Crab Nebula in the regions of M33 surveyed, but we have found an X-ray source with a power law spectrum coincident with a small-diameter radio source that may be the first pulsar-wind nebula recognized in M33.
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