We present the detection of the first candidate colliding-wind binary (CWB) in M33, located in the giant H II region NGC 604. The source was first identified in archival {it Chandra} imaging as a relatively soft X-ray point source, with the likely primary star determined from precise astrometric alignment between archival {it Hubble Space Telescope} and {it Chandra} imaging. The candidate primary star in the CWB is classified for the first time in this work as a carbon-rich Wolf-Rayet star with a likely O star companion based on spectroscopy obtained from Gemini-North. We model the X-ray spectrum using {it Chandra} and {it XMM-Newton} observations, and find the CWB is well-fit as a $sim$ 1 keV thermal plasma with a median unabsorbed luminosity in the 0.5--2.0 keV band of $L_{rm X}$ $sim$ 3 $times$ 10$^{35}$ erg s$^{-1}$, making this source among the brightest of CWBs observed to date. We present a long term light curve for the candidate CWB from archival {it Chandra} and {it XMM-Newton} observations, and discuss the constraints placed on the binary by this light curve, as well as the X-ray luminosity at maximum. Finally, we compare this candidate CWB in M33 to other well-studied, bright CWBs in the Galaxy and Magellanic Clouds, such as $eta$ Car.
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