  To cosmic rays incident near the horizon the Earth's atmosphere represents a
beam dump with a slant depth reaching 36000~g~cm$^{-2}$ at $90^\circ$. The
prompt decay of a heavy quark produced by very high energy cosmic ray showers
will leave an unmistakable signature in this dump. We translate the failure of
experiments to detect such a signal into an upper limit on the heavy quark
hadroproduction cross section in the energy region beyond existing
accelerators. Our results disfavor any rapid growth of the cross section or the
gluon structure function beyond very conservative estimates based on
perturbative QCD.
