We present ~103 ks of Chandra observations of the galaxy cluster SPT-CLJ0528-5300 (SPT0528, z=0.768). This cluster harbors the most radio-loud (L_1.4GHz = 1.01 x 10^33 erg/s/Hz) central AGN of any cluster in the South Pole Telescope (SPT) SZ survey with available X-ray data. We find evidence of AGN-inflated cavities in the X-ray emission, which are consistent with the orientation of the jet direction revealed by ATCA radio data. The combined probability that two such depressions -- each at ~1.4-1.8sigma significance, oriented ~180 degrees apart and aligned with the jet axis -- would occur by chance is 0.1%. At >10^61 erg, the outburst in SPT0528 is among the most energetic known in the universe, and certainly the most powerful known at z>0.25. This work demonstrates that such powerful outbursts can be detected even in shallow X-ray exposures out to relatively high redshifts (z~0.8), providing an avenue for studying the evolution of extreme AGN feedback. The ratio of the cavity power (P_cav = 9.4+/-5.8 x 10^45 erg/s) to the cooling luminosity (L_cool = 1.5+/-0.5 x 10^44 erg/s) for SPT0528 is among the highest measured to date. If, in the future, additional systems are discovered at similar redshifts with equally high P_cav/L_cool ratios, it would imply that the feedback/cooling cycle was not as gentle at high redshifts as in the low-redshift universe.
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