Evidence is reported for a narrow structure near the J/psi
phi threshold in exclusive B+ --> J/psi phi K+ decays produced in p
anti-p collisions at s**(1/2) ñ.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 +/- 1.2(syst) MeV/c2
and 11.7+8.3_-5.0(stat) +/- 3.7(syst) MeV/c2.