We report the Chandra detection of shock-heated shells of hot gas surrounding the radio lobes of the nearby ( D _ { L } \sim 53 Mpc ) low-power radio galaxy NGC 3801 . The shells have temperatures of 1 keV and 0.7 keV , compared to an ISM temperature of 0.23 keV . The estimated expansion speed of the shells is \sim 850 km s ^ { -1 } , corresponding to a Mach number of \sim 4 . This is the second X-ray detection of strong shocks produced by a low-power radio galaxy , and allows us to measure directly the contribution of shock heating to the radio galaxy ’ s total energetic input to the ISM . We show that the gas properties of the shells and surrounding ISM are consistent with the Rankine-Hugoniot shock jump conditions . We estimate the energy stored in the hot gas shells ( thermal + kinetic energy ) to be 1.7 \times 10 ^ { 56 } ergs , which is equivalent to the thermal energy of the ISM within \sim 11 kpc of the galaxy centre , and a factor of \sim 25 larger than the inferred P d V work required to inflate the lobe cavities , indicating that energy transfer from the AGN to its environment is dominated by shock heating during this stage of radio-source evolution . Our results provide direct evidence that shock heating in the early supersonic phase of FRI radio-source expansion can have important long-term effects on the properties of the host galaxy ISM . Finally , we discuss the merger history of NGC 3801 , the fuelling of its AGN and the role of this type of system in feedback models .