The X-ray properties of a relaxed cluster of galaxies are determined primarily by its gravitational potential well and the entropy distribution of its intracluster gas. That entropy distribution reflects both the accretion history of the cluster and the feedback processes which limit the condensation of intracluster gas. Here we present Chandra observations of the core entropy profiles of nine classic cooling-flow clusters that appear relaxed and contain intracluster gas with a cooling time less than a Hubble time. We show that those entropy profiles are remarkably similar, despite the fact that the clusters range over a factor of three in temperature. They typically have an entropy level of ~ 130 keV cm^2 at 100 kpc that declines to a plateau ~10 keV cm^2 at lesssim 10 kpc. Between these radii, the entropy profiles are propto r^alpha with alpha ~ 1.0 - 1.3. The non-zero central entropy levels in these clusters correspond to a cooling time ~10^8 yr, suggesting that episodic heating on this timescale maintains the central entropy profile in a quasi-steady state.
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