We present the first search for heavy, long-lived particles that decay to photons at a hadron collider. We use a sample of gamma + jet + missing transverse energy events in pp[over] collisions at square root[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 [Formula: see text] and place the world-best 95% C.L. lower limit on the [Formula: see text] mass of 101 GeV/c(2) at [Formula: see text].