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A precision measurement of the mass of the h_c(1P1) state of charmonium hasbeen made using a sample of 24.5 million psi(2S) events produced in e+e-annihilation at CESR. The reaction used was psi(2S) -> pi0 h_c, pi0 -> gammagamma, h_c -> gamma eta_c, and the reaction products were detected in theCLEO-c detector.  Data have been analyzed both for the inclusive reaction and for the exclusivereactions in which eta_c decays are reconstructed in fifteen hadronic decaychannels. Consistent results are obtained in the two analyses. The averagedresults of the present measurements are M(h_c)=3525.28+-0.19 (stat)+-0.12(syst)MeV, and B(psi(2S) -> pi0 h_c)xB(h_c -> gamma eta_c)= (4.19+-0.32+-0.45)x10^-4.Using the 3PJ centroid mass, Delta M_hf(1P)=<M(chi_cJ)> - M(h_c) =+0.02+-0.19+-0.13 MeV.

Precision Measurement of the Mass of the h_c(1P1) State of Charmonium