  Recent observations have revealed the existence of an enormously energetic >
10^61 erg AGN outburst in the Hydra A cluster of galaxies. This outburst has
produced cavities in the intra-cluster medium, apparently supported by pressure
from cosmic rays. Here we argue that if these cavities are filled with > GeV
particles, these particles are very likely protons and nuclei. For a plausible
spatial distribution of the target gas, based on observations and
hydrodynamical simulations, we show that the pi^0-decay gamma-rays from these
cosmic-rays may be detectable with the H.E.S.S.experiment.
