We present the results of the first hadron collider search for heavy, long-lived neutralinos that decay via chi(0)(1)->gamma G in gauge-mediated supersymmetry breaking models. Using an integrated luminosity of 570 +/- 34 pb(-1) of p (p) over bar collisions at root s=1.96 TeV, we select gamma+jet+missing transverse energy candidate events based on the arrival time of a high-energy photon at the electromagnetic calorimeter as measured with a timing system that was recently installed on the CDF II detector. We find 2 events, consistent with the background estimate of 1.3 +/- 0.7 events. While our search strategy does not rely on model-specific dynamics, we set cross section limits and place the world-best 95% C.L. lower limit on the chi(0)(1) mass of 101 GeV/c(2) at tau(0)(chi 1)=5 ns. RI Ruiz, Alberto/E-4473-2011; Robson, Aidan/G-1087-2011; De Cecco, Sandro/B-1016-2012; Prokoshin, Fedor/E-2795-2012