  We present first results on the cooling properties derived from Chandra X-ray
observations of 83 high-redshift (0.3 < z < 1.2) massive galaxy clusters
selected by their Sunyaev-Zel'dovich signature in the South Pole Telescope
data. We measure each cluster's central cooling time, central entropy, and mass
deposition rate, and compare to local cluster samples. We find no significant
evolution from z~0 to z~1 in the distribution of these properties, suggesting
that cooling in cluster cores is stable over long periods of time. We also find
that the average cool core entropy profile in the inner ~100 kpc has not
changed dramatically since z ~ 1, implying that feedback must be providing
nearly constant energy injection to maintain the observed "entropy floor" at
~10 keV cm^2. While the cooling properties appear roughly constant over long
periods of time, we observe strong evolution in the gas density profile, with
the normalized central density (rho_0/rho_crit) increasing by an order of
magnitude from z ~ 1 to z ~ 0. When using metrics defined by the inner surface
brightness profile of clusters, we find an apparent lack of classical, cuspy,
cool-core clusters at z > 0.75, consistent with earlier reports for clusters at
z > 0.5 using similar definitions. Our measurements indicate that cool cores
have been steadily growing over the 8 Gyr spanned by our sample, consistent
with a constant, ~150 Msun/yr cooling flow that is unable to cool below
entropies of 10 keV cm^2 and, instead, accumulates in the cluster center. We
estimate that cool cores began to assemble in these massive systems at z ~ 1,
which represents the first constraints on the onset of cooling in galaxy
cluster cores. We investigate several potential biases which could conspire to
mimic this cool core evolution and are unable to find a bias that has a similar
redshift dependence and a substantial amplitude.
