We present the results of the first hadron collider search for heavy, long-lived neutralinos that decay via χ˜01→γG˜ in gauge-mediated supersymmetry breaking models. Using an integrated luminosity of 570±34  pb−1 of pp collisions at s√=1.96  TeV, we select γ+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 χ˜01 mass of 101  GeV/c2 at τχ˜01=5  ns.