We report the observation of a narrow state decaying into J/psipi+pi- and produced in 220 pb(-1) of p p-bar collisions at =1.96 Tesqaure root of sV 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.