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We present the results of a search for anomalous production of diphoton events with large missing transverse energy using the Collider Detector at Fermilab. In 202 pb-1 of pp̅ collisions at √s =1.96 TeV we observe no candidate events, with an expected standard model background of 0.27±0.07(stat)±0.10(syst) events. The results exclude a lightest chargino of mass less than 167 GeV/c2, and lightest neutralino of mass less than 93 GeV/c2 at 95% C.L. in a gauge-mediated supersymmetry-breaking model with a light gravitino.