Hadronic transitions of the charmonium 1P1 (=h(c)) state into J/psi are considered in the QCD multipole expansion. Using the decay rate of CHI(cJ) --> J/psi + gamma and a quantum-mechanical sum rule, we estimate GAMMA(h(c)(1P)-->J/psipi0) > 1.6 keV, which is close to the recent measurement by E760, GAMMA(h(c)(1P)-->J/psipi0) approximately 1 keV. Other transitions of h(c) are also considered in the same context.