[en] The authors present the results of the first hadron collider search for heavy, long-lived neutralinos that decay via (tilde χ)₁⁰ → γ(tilde G) in gauge-mediated supersymmetry breaking models. Using an integrated luminosity of 570 ± 34 pb^-1 of p(bar p) collisions at √s = 1.96 TeV, they 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. They find 2 events, consistent with the background estimate of 1.3 ± 0.7 events. While the search strategy does not rely on model-specific dynamics, they set cross section limits and place the world-best 95% C.L. lower limit on the (tilde χ)₁⁰ mass of 101 GeV/c² at τ_#tilde _χ)#sub 1#_#sup 0# = 5 ns