  Unitarity relates the total cross section for neutrino-nucleon scattering to
the neutrino-nucleon forward scattering amplitude. Assuming the validity of the
perturbative expansion of the forward amplitude in the {\em weak} coupling
constant, we derive a unitarity bound on the inelastic cross section. The
inelastic cross section saturates this bound at a typical neutrino energy
$E_\nu \simeq 10^8 {\rm GeV}$. This implies that calculations of the inelastic
cross section that use current parton distribution functions and lowest order
weak perturbation theory are unreliable above this energy.
