  The first observations conducted as part of the Chandra ACIS survey of M 33
(ChASeM33) sampled the eclipsing X-ray binary M 33 X-7 over a large part of the
3.45 d 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 (2453639.119+-0.005)
+- N x (3.453014+-0.000020) and constrain the eclipse half angle to (26.5+-1.1)
degree. 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 O6III star with the help of extinction and colour 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_sun. This mass, the
shape of the X-ray spectrum and the short term X-ray time variability identify
M 33 X-7 as the first eclipsing black hole high mass X-ray binary.
