We present results of a search for supernova remnants (SNRs) in archival Chandra images of M33. We have identified X-ray SNRs by comparing the list of Chandra, X-ray sources in M33 with tabulations of SNR candidates identified from (1) elevated [S II]/Halpha ratios in the optical, and (2) radio spectral indices. Of the 98 optically known SNRs in M33, 22 have been detected at > 3-sigma level in the soft band (0.35-1.1 keV). At least four of these SNR candidates are spatially extended based on a comparison of the data to simulated images of point sources. Aside from the optically matching SNRs, we have found one soft X-ray source in M33 which exhibits no optical emission and is coincident with a known radio source. The radio spectral index of this source is consistent with particle acceleration in shocks, leading us to suggest that it is a non-radiative SNR. We have also found new optical counterparts to two soft X-ray SNRs in M33. Pending confirmation from optical spectroscopy, the identification of these two optical counterparts increases the total number of known optically emitting SNRs in M33 to 100. This brings the total number of identified SNRs with X-ray counterparts, including those exclusively detected by the XMM-Newton survey of M33, to 37 SNRs. We find that while there are a similar number of confirmed X-ray SNRs in M33 and the LMC with X-ray luminosities in excess of 1e35 ergs/s, nearly 40% of the LMC SNRs are brighter than 1e36 ergs/s, while only 13% of the M33 sample exceed this luminosity. The differences in luminosity distributions cannot be fully explained by uncertainty in spectral model parameters, and is not fully accounted for by abundance differences between the galaxies (abridged).
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