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.
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