  From e+e- collision data acquired with the CLEO-c detector at CESR, we search
for the non-DDbar decays psi(3770) -> gamma chi_cJ, with chi_cJ reconstructed
in four exclusive decays modes containing charged pions and kaons. We report
the first observation of such decays for J=0 with a branching ratio of
(0.73+-0.07+-0.06)%. The rates for different J are consistent with the
expectations assuming psi(3770) is predominantly a 1^3D_1 state of charmonium,
but only if relativistic corrections are applied.
