The decays χc1→J/ψμ+μ- and χc2→J/ψμ+μ- are observed and used to study the resonance parameters of the χc1 and χc2 mesons. The masses of these states are measured to be m(χc1)=3510.71±0.04(stat)±0.09(syst) MeV and m(χc2)=3556.10±0.06(stat)±0.11(syst) MeV, where the knowledge of the momentum scale for charged particles dominates the systematic uncertainty. The momentum-scale uncertainties largely cancel in the mass difference m(χc2)-m(χc1)=45.39±0.07(stat)±0.03(syst) MeV. The natural width of the χc2 meson is measured to be Γ(χc2)=2.10±0.20(stat)±0.02(syst) MeV. These results are in good agreement with and have comparable precision to the current world averages.