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 these properties to those for 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 ~100kpc has not changed dramatically since z~1, implying that feedback must be providing nearly constant energy injection to maintain the observed "entropy floor" at ~10keV cm^2^.