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We report the observation of a narrow state decaying into J/ψ π+ π- and produced in 220 pb-1 of p̅p collisions at √s =1.96 TeV in the CDF II experiment. We observe 730±90 decays. The mass is measured to be 3871.3±0.7(stat)±0.4(syst) MeV/c2, with an observed width consistent with the detector resolution. This is in agreement with the recent observation by the Belle Collaboration of the X(3872) meson.