Using a sample of 2.59 times 10^7 psi(2S) decays collected by the CLEO--c detector, we present results of a study of chi_{cJ} (J=0,1,2) decays into baryon-antibaryon final states. We present the worlds most precise measurements of the chi_cJ -> p-pbar and chi_cJ -> Lambda-Lambdabar branching fractions, and the first measurements of chi_c0 decays to other hyperons. These results illuminate the decay mechanism of the chi_c states.