We consider the possibility that supersymmetry is broken above the inflationary mass scale and that the only "low" energy remnant of supersymmetry is the gravitino with a mass of the order of the EeV scale. The gravitino in this class of models becomes a candidate for the dark matter of the Universe. To avoid the overproduction of gravitinos from the decays of the next-to-lightest supersymmetric particle we argue that the supersymmetric spectrum must lie above the inflationary mass scale (MSUSY>10-5MP∼1013 GeV). Since m3/2≃MSUSY2/MP, we expect m3/2≳0.2 EeV. Cosmological constraints then predict a relatively large reheating temperature between 1010 and 1012 GeV.