We report the Chandra detection of a large-scale shock , on scales of 200 kpc , in the cluster surrounding the powerful radio galaxy 3C 444 ( PKS 2211 - 17 ) . Our 20-ks Chandra observation allows us to identify a clear surface brightness drop around the outer edge of the radio galaxy , which is likely to correspond to a spheroidal shock propagating into the intracluster medium . We measure a temperature jump across the surface brightness drop of a factor \sim 1.7 , which corresponds to a Mach number of \sim 1.7 . This is likely to be an underestimate due to the need to average over a fairly large region when measuring the temperature of the post-shock gas . We also detect clear cavities corresponding to the positions of the radio lobes , which is only the second such detection associated with an FRII radio galaxy . We estimate that the total energy transferred to the environment is at least 8.2 \times 10 ^ { 60 } ergs , corresponding to a jet power of > 2.2 \times 10 ^ { 45 } ergs s ^ { -1 } ( assuming a timescale based on the measured shock speed ) . We also compare the external pressure acting on the lobes with the internal pressure under various assumptions , and conclude that a significant contribution from protons is required .