A peaking structure in the J/psi phi mass spectrum near threshold is observed in B(+/-) to J/psi phi K(+/-) decays, produced in pp collisions at sqrt(s) = 7 TeV collected with the CMS detector at the LHC. The data sample, selected on the basis of the dimuon decay mode of the J/psi, corresponds to an integrated luminosity of 5.2 inverse femtobarns. Fitting the structure to an S-wave relativistic Breit-Wigner lineshape above a three-body phase-space nonresonant component gives a signal statistical significance exceeding five standard deviations. The fitted mass and width values are m=4148.0 +/- 2.4 (stat.) +/- 6.3 (syst.) MeV and Gamma=28 -11+15 (stat.) +/- 19 (syst.) MeV, respectively. Evidence for an additional peaking structure at higher J/psi phi mass is also reported.