  We present an analysis of a Chandra ACIS-I observation of the massive galaxy
cluster A644. This cluster was previously classified as a cooling flow, but no
radio emission has been detected from its cD galaxy. Outside the core (R ~75
kpc ~0.03R_vir) the hot ICM has properties consistent with a (relaxed)
cool-core cluster out to the largest radii investigated (R ~415 kpc ~0.14
R_vir). Over this region the gravitating mass profile is described well by a
Navarro-Frenk-White profile with concentration parameter, c = 6.1 +/- 1.2, and
virial radius, R_vir = 2.9 +/- 0.4 Mpc. However, inside the core the
temperature and entropy profiles reverse their inward radial decline and rise
at the center; the inner temperature profile is inconsistent with a constant at
the 2.3 sigma level. Although the core region does not display X-ray cavities
or filamentary structures characteristic of radio-loud, cool-core clusters, the
peak of the X-ray emission is offset from that of the centroid of the global
X-ray halo by ~60 kpc. The position of the cD galaxy lies approximately between
the X-ray peak and centroid, further testifying to a merger origin for the
properties of the X-ray emission in the core. We discuss the implications of
A644 and the small number of radio-quiet, cool-core clusters for the AGN
feedback paradigm to suppress cooling flows in clusters.
