From e(+)e(-) collision data acquired with the CLEO-c detector at CESR, we search for the non-D (D) over bar 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(3)D(1) state of charmonium, but only if relativistic corrections are applied.