In this Letter we report on a search for long-lived particles that decay into final states with two electrons or photons. Such long-lived particles arise in a variety of theoretical models, like hidden valleys and supersymmetry with gauge-mediated breaking. By precisely reconstructing the direction of the electromagnetic shower we are able to probe much longer lifetimes than previously explored. We see no evidence of the existence of such long-lived particles and interpret this search as a quasi model-independent limit on their production cross section, as well as a limit on a long-lived fourth generation quark.