We present the first search for heavy, long-lived particles that decay to photons at a hadron collider. We use a sample of γ+jet+missing transverse energy events in pp collisions at s√=1.96  TeV taken with the CDF II detector. Candidate events are selected based on the arrival time of the photon at the detector. Using an integrated luminosity of 570  pb−1 of collision data, we observe 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 in a supersymmetric model with χ˜01→γG˜ and place the world-best 95% C.L. lower limit on the χ˜01 mass of 101  GeV/c2 at τχ˜01=5  ns.