Rigorous QCD predictions for the decay rates of the P-wave states of heavy quarkonia are presented. They are based on a new factorization theorem which is valid to leading order in the heavy-quark velocity and to all orders in the running coupling constant of QCD. The decay rates for all four P states into light-hadronic or electromagnetic final states axe expressed in terms of two phenomenological parameters, whose coefficients axe perturbatively calculable. Logarithms of the binding energy encountered in previous perturbative calculations of P-wave decays are factored into a phenomenological parameter that is related to the probability for the heavy-quark-antiquark pair to be in a color-octet S-wave state. Applying these predictions to charmonium, we use measured decay rates for the chi(c1) and chi(c2) to predict the decay rates of the chi(c0) and h(c).