  We discuss a scenario in which the highest energy cosmic rays (CR's) and
cosmological $\gamma$-ray bursts (GRB's) have a common origin. This scenario is
consistent with the observed CR flux above $10^{20}\text{eV}$, provided that
each burst produces similar energies in $\gamma$-rays and in CR's above
$10^{20}\text{eV}$. Protons may be accelerated by Fermi's mechanism to energies
$\sim10^{20}\text{eV}$ in a dissipative, ultra-relativistic wind, with
luminosity and Lorentz factor high enough to produce a GRB. For a homogeneous
GRB distribution, this scenario predicts an isotropic, time-independent CR
flux.
