  We consider the effects of R-parity violation due to the inclusion of a
bilinear $\mu^\prime L H_u$ superpotential term in high scale supersymmetric
models with an EeV scale gravitino as dark matter. Although the typical
phenomenological limits on this coupling (e.g. due to lepton number violation
and the preservation of the baryon asymmetry) are relaxed when the
supersymmetric mass spectrum is assumed to be heavy (in excess of the
inflationary scale of $3 \times 10^{13}$ GeV), the requirement that the
gravitino be sufficiently long-lived so as to account for the observed dark
matter density, leads to a relatively strong bound on $\mu^\prime \lesssim 20$
GeV. The dominant decay channels for the longitudinal component of the
gravitino are $Z \nu, W^\pm l^\mp$, and $h\nu$. To avoid an excess neutrino
signal in IceCube, our limit on $\mu'$ is then strengthened to $\mu' \lesssim
50$ keV. When the bound is saturated, we find that there is a potentially
detectable flux of mono-chromatic neutrinos with EeV energies.
