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 pp 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.