  A sufficiently magnetized Local Supercluster can explain the spectrum and
angular distribution of ultra-high energy cosmic rays. We show that the
spectrum of extragalactic cosmic rays with energies below $\sim 10^{20}$ eV may
be due to the diffusive propagation in the Local Supercluster with fields of
$\sim 10^{-8} - 10^{-7}$ Gauss. Above $\sim 10^{20}$ eV, cosmic rays propagate
in an almost rectilinear way which is evidenced by the change in shape of the
spectrum at the highest energies. The fit to the spectrum requires that at
least one source be located relatively nearby at $\sim 10-15$ Mpc away from the
Milky Way. We discuss the origin of magnetic fields in the Local Supercluster
and the observable predictions of this model.
