  We present an analysis of a 41 ks Chandra observation of the merging cluster
Abell 2065 with the ACIS-I detector. Previous observations with ROSAT and ASCA
provided evidence for an ongoing merger, but also suggested that there were two
surviving cooling cores, which were associated with the two cD galaxies in the
center of the cluster. The Chandra observation reveals only one X-ray surface
brightness peak, which is associated with the more luminous, southern cD
galaxy. The gas related with that peak is cool and displaced slightly from the
position of the cD. The data suggest that this cool material has formed a cold
front. On the other hand, in the higher spatial resolution Chandra image, the
second feature to the north is not associated with the northern cD; rather, it
appears to be a trail of gas behind the main cD. We argue that only one of the
two cooling cores has survived the merger, although it is possible that the
northern cD may not have possessed a cool core prior to the merger. We use the
cool core survival to constrain the kinematics of the merger and we find an
upper limit of ~< 1900 km/s for the merger relative velocity. A surface
brightness discontinuity is found at ~140 kpc from the southern cD; the Mach
number for this feature is ${\cal M} = 1.66^{+0.24}_{-0.32}$, although its
nature (shock or cold front) is not clear from the data. We argue that Abell
2065 is an example of an unequal mass merger. The more massive southern cluster
has driven a shock into the ICM of the infalling northern cluster, which has
disrupted the cool core of the latter, if one existed originally. We estimate
that core crossing occurred a few hundred Myr ago, probably for the first time.
