  We consider supersymmetric models where the scale of supersymmetry breaking
lies between 5 $\times 10^6$ GeV and 5 $\times 10^8$ GeV. In this class of
theories, which includes models of gauge mediated supersymmetry breaking, the
lightest supersymmetric particle is the gravitino. The next to lightest
supersymmetric particle is typically a long lived charged slepton with a
lifetime between a microsecond and a second, depending on its mass. Collisions
of high energy neutrinos with nucleons in the earth can result in the
production of a pair of these sleptons. Their very high boost means they
typically decay outside the earth. We investigate the production of these
particles by the diffuse flux of high energy neutrinos, and the potential for
their observation in large ice or water Cerenkov detectors. The relatively
small cross-section for the production of supersymmetric particles is partially
compensated for by the very long range of heavy particles. The signal in the
detector consists of two parallel charged tracks emerging from the earth about
100 meters apart, with very little background. A detailed calculation using the
Waxman-Bahcall limit on the neutrino flux and realistic spectra shows that
km$^3$ experiments could see as many as 4 events a year. We conclude that
neutrino telescopes will complement collider searches in the determination of
the supersymmetry breaking scale, and may even give the first evidence for
supersymmetry at the weak scale.
