The first observations conducted as part of the Chandra ACIS survey of M33 (ChASeM33) sampled the eclipsing X-ray binary M33 X-7 over a large part of the 3.45 day orbital period and have resolved eclipse ingress and egress for the first time. The occurrence of the X-ray eclipse allows us to determine an improved ephemeris of mid-eclipse and binary period as HJD (2,453,639.119 ± 0.005) ± N(3.453014 ± 0.000020) and constrain the eclipse half-angle to 265 ± 11. There are indications for a shortening of the orbital period. The X-ray spectrum is best described by a disk blackbody spectrum typical for black hole X-ray binaries in the Galaxy. We find a flat power density spectrum, and no significant regular pulsations were found in the frequency range of 10-4 to 0.15 Hz. HST WFPC2 images resolve the optical counterpart, which can be identified as an O6 III star with the help of extinction and color corrections derived from the X-ray absorption. Based on the optical light curve, the mass of the compact object in the system most likely exceeds 9 M☉. This mass, the shape of the X-ray spectrum, and the short-term X-ray time variability identify M33 X-7 as the first eclipsing black hole high-mass X-ray binary.
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