We present the results of a search for supersymmetry with gauge-mediated breaking and χ˜01→γG˜ in the γγ+missing transverse energy final state. In 2.6±0.2  fb−1 of pp collisions at s√=1.96  TeV recorded by the CDF II detector we observe no candidate events, consistent with a standard model background expectation of 1.4±0.4 events. We set limits on the cross section at the 95% C.L. and place the world's best limit of 149  GeV/c2 on the χ˜01 mass at τχ˜01≪1  ns. We also exclude regions in the χ˜01 mass-lifetime plane for τχ˜01≲2  ns.