We search for inclusive high ETdiphoton events with large missing transverse energy in pp¯collisions at s=1.8 TeV. Such events are expected from pair production of charginos and neutralinos within the framework of the minimal supersymmetric standard model with a light gravitino. No excess of events is observed. In that model, and assuming gaugino mass unification at the GUT scale, we obtain a 95% C.L. exclusion region in the supersymmetry parameter space and lower mass bounds of 150 GeV/c2for the lightest chargino and 77GeV/c2for the lightest neutralino.