The decays χ_{c1}→J/ψμ^{+}μ^{-} and χ_{c2}→J/ψμ^{+}μ^{-} are observed and used to study the resonance parameters of the χ_{c1} and χ_{c2} mesons. The masses of these states are measured to be m(χ_{c1})=3510.71±0.04(stat)±0.09(syst) MeV and m(χ_{c2})=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(χ_{c2})-m(χ_{c1})=45.39±0.07(stat)±0.03(syst) MeV. The natural width of the χ_{c2} meson is measured to be Γ(χ_{c2})=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.