We present the results of a search for supersymmetry with gauge-mediated breaking and (chi) over tilde (1)(0) -> gamma(G) over tilde in the gamma gamma + missing transverse energy final state. In 2.6 +/- 0.2 fb(-1) of p (p) over bar collisions at root 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/c(2) on the (chi) over tilde (1)(0) mass at tau((chi) over tilde 01) << 1 ns. We also exclude regions in the (chi) over tilde (1)(0) mass-lifetime plane for tau((chi) over tilde 01) less than or similar to 2 ns. RI De Cecco, Sandro/B-1016-2012; Robson, Aidan/G-1087-2011; St.Denis, Richard/C-8997-2012; Prokoshin, Fedor/E-2795-2012; Ruiz, Alberto/E-4473-2011