We present results from a 57.6 ks Chandra observation of the cluster gas associated with the fat-double radio galaxy 3C 310. We find a surface brightness discontinuity in the gas outside the southern radio lobe that we attribute to a shock driven by the supersonic inflation of this lobe ~180 kpc from the nucleus. Modeling the surface brightness/density jump, the shock has Mach number 1.5-1.9, depending on the assumptions one makes about the density profile and the nature of the energy input. There are not sufficient counts in the image to detect conclusively the temperature jump associated with the shock. The total mechanical energy of the outburst is 5 × 1060 erg. Assuming a Mach 1.9 shock, the age of the outburst is ~100 million yrs, and the time-averaged power of the outburst is ~1.3 × 1045 erg s–1. The power input is 100 times greater than the radiative losses of the gas within the radius of the shock. Most importantly, the equivalent heat input due to the entropy increase is roughly 10% of the thermal energy of the gas to the radius of the shock. 3C 310 is another example where regular outbursts of the observed strength with a duty cycle of 0.1 could offset the radiative losses of the gas near the Bondi radius and regulate feedback. We also detect a cool filamentary X-ray arm along the eastern periphery of the southern radio lobe. This arm is probably composed of low-entropy gas dredged up in the inflation of the radio plasma, similar to features seen in M87.