  We present an analysis of a 72 ks Chandra observation of the double cluster
Abell 1644 (z=0.047). The X-ray temperatures indicate the masses are
M500=2.6+/-0.4 x10^{14} h^{-1} M_sun for the northern subcluster and
M500=3.1+/-0.4 x10^{14} h^{-1} M_sun for the southern, main cluster. We
identify a sharp edge in the radial X-ray surface brightness of the main
cluster, which we find to be a cold front, with a jump in temperature of a
factor of ~3. This edge possesses a spiral morphology characteristic of core
gas sloshing around the cluster potential minimum. We present observational
evidence, supported by hydrodynamic simulations, that the northern subcluster
is the object which initiated the core gas sloshing in the main cluster at
least 700 Myr ago. We discuss reheating of the main cluster's core gas via two
mechanisms brought about by the sloshing gas: first, the release of
gravitational potential energy gained by the core's displacement from the
potential minimum, and second, a dredging inwards of the outer, higher entropy
cluster gas along finger-shaped streams. We find the available gravitational
potential energy is small compared to the energy released by the cooling gas in
the core.
