Evidence is reported for a narrow structure near the J/ψϕ threshold in exclusive B+→J/ψϕK+ decays produced in pp collisions at s√=1.96  TeV. A signal of 14±5 events, with statistical significance in excess of 3.8 standard deviations, is observed in a data sample corresponding to an integrated luminosity of 2.7  fb−1, collected by the CDF II detector. The mass and natural width of the structure are measured to be 4143.0±2.9(stat)±1.2(syst)  MeV/c2 and 11.7+8.3−5.0(stat)±3.7(syst)  MeV/c2.