We present results from a 35 ks Chandra /ACIS-I observation of the hot ICM around the FR II radio galaxy 3C 388 .
3C 388 resides in a cluster environment with an ICM temperature of \sim 3.5 keV .
We detect cavities in the ICM coincident with the radio lobes .
The enthalpy of these cavities is \sim 1.2 \times 10 ^ { 60 } ergs .
The work done on the gas by the inflation of the lobes is \sim 3 \times 10 ^ { 59 } ergs , or \sim 0.87 keV per particle out to the radius of the lobes .
The radiative timescale for gas at the center of the cluster at the current temperature is a few Gyrs .
The gas in the core was probably cooler and denser before the outburst , so the cooling time was considerably shorter .
We are therefore likely to be witnessing the quenching of a cluster cooling flow by a radio galaxy outburst .
The mechanical power of the lobes is at least 20 times larger than the radiative losses out to the cooling radius .
Outbursts of similar power with a \sim 5 % duty cycle would be more than sufficient to continually reheat the cluster core over the Hubble time and prevent the cooling of any significant amount of gas .
The mechanical power of the outburst is also roughly two orders of magnitude larger than either the X-ray luminosity of the active nucleus or the radio luminosity of the lobes .
The equipartition pressure of the radio lobes is more than an order of magnitude lower than that of the ambient medium , indicating that the pressure of the lobe is dominated by something other than the relativistic electrons radiating at GHz frequencies .