  Interactions of cosmic rays with the interstellar gas and radiation fields of
the Milky Way provide the majority of the gamma rays observed by the Fermi
Gamma Ray Space Telescope. In addition to the gas which is densely concentrated
along the Galactic Disk, hydrodynamical simulations and observational evidence
favor the presence of a halo of hot (T~10^6 K) ionized hydrogen (H_II),
extending with non-negligible densities out to the virial radius of the Milky
Way. We show that cosmic ray collisions with this circum-galactic gas should be
expected to provide a significant flux of gamma rays, on the order of 10% of
the observed isotopic gamma ray background at energies above 1 GeV. In
addition, gamma rays originating from the extended H_II halos of other galaxies
along a given line-of-sight should contribute to this background at a similar
level.
