We report on a study of exclusive radiative decays of the '(1S) resonance. We have considered decays into final states of the form n(h+h-), with (h+h-) denoting a charged-hadron pair (either +-, K+K-, or pp»), and n denoting the number of such pairs in the event. We measure branching ratios for n=2, 3, and 4, and search for structure in the recoiling hadronic system. For the n=1 case, we present upper limits. No evidence is observed for two-body radiative decays of the '(1S) meson in any of the above channels.