  Evidence is reported for a narrow structure near the $J/\psi\phi$ threshold
in exclusive $B^+\to J/\psi\phi K^+$ decays produced in $\bar{p} p $ collisions
at $\sqrt{s}=1.96 \TeV$. A signal of $14\pm5$ events, with statistical
significance in excess of 3.8 standard deviations, is observed in a data sample
corresponding to an integrated luminosity of $2.7 \ifb$, collected by the CDF
II detector. The mass and natural width of the structure are measured to be
$4143.0\pm2.9(\mathrm{stat})\pm1.2(\mathrm{syst}) \MeVcc$ and
$11.7^{+8.3}_{-5.0}(\mathrm{stat})\pm3.7(\mathrm{syst}) \MeVcc$.
