The radio source Hercules A resides at the center of a cooling flow cluster of galaxies at redshift z = 0.154. A Chandra X-ray image reveals a shock front in the intracluster medium (ICM) surrounding the radio source, about 160 kpc from the active galactic nucleus (AGN) that hosts it. The shock has a Mach number of 1.65, making it the strongest of the cluster-scale shocks driven by an AGN outburst found so far. The age of the outburst is 5.9 × 107 yr, its energy ~3 × 1061 ergs, and its mean power ~1.6 × 1046 ergs s-1. As for the other large AGN outbursts in cooling flow clusters, this outburst overwhelms radiative losses from the ICM of the Hercules A Cluster by a factor of ~100. It adds to the case that AGN outbursts are a significant source of preheating for the ICM. Unless the mechanical efficiency of the AGN in Hercules A exceeds 10%, the central black hole must have grown by more than 1.7 × 108 M☉ to power this one outburst.