We present the results of Chandra X-ray observations of the isolated , massive , compact , relic galaxies MRK 1216 and PGC 032873 . Compact massive galaxies observed at z > 2 , also called red nuggets , formed in quick dissipative events and later grew by dry mergers into the local giant ellipticals . Due to the stochastic nature of mergers , a few of the primordial massive galaxies avoided the mergers and remained untouched over cosmic time . We find that the hot atmosphere surrounding MRK 1216 extends far beyond the stellar population and has an 0.5–7 keV X-ray luminosity of L _ { X } = ( 7.0 \pm 0.2 ) \times 10 ^ { 41 } erg s ^ { -1 } , which is similar to the nearby X-ray bright giant ellipticals . The hot gas has a short central cooling time of \sim 50 Myr and the galaxy has a \sim 13 Gyr old stellar population . The presence of an X-ray atmosphere with a short nominal cooling time and the lack of young stars indicate the presence of a sustained heating source , which prevented star formation since the dissipative origin of the galaxy 13 Gyrs ago . The central temperature peak and the presence of radio emission in the core of the galaxy indicate that the heating source is radio-mechanical AGN feedback . Given that both MRK 1216 and PGC 032873 appear to have evolved in isolation , the order of magnitude difference in their current X-ray luminosity could be traced back to a difference in the ferocity of the AGN outbursts in these systems . Finally , we discuss the potential connection between the presence of hot halos around such massive galaxies and the growth of super/over-massive black holes via chaotic cold accretion .