chi(cJ) decays to h(+)h(-)h(0)

Using a sample of 3 X 10(6) psi(2S) decays recorded by the CLEO detector, we study three-body decays of the X(c)0, X-c1, and X-c2 produced in radiative decays of the psi(2S). We consider the final states pi(+) pi(-) eta, K+ K- eta pp eta, pi(+) pi(-) eta', K+ K- pi(0), pp pi(0), pi(+) K- K-S(0) and K+ p Lambda , measuring branching fractions or placing upper limits. For X-c1 -> pi(+) pi(-) eta, K+ K- pi(0), and pi(+) K- K-S(0) our observed samples are large enough to indicate the largest contributions to the substructure.