A peaking structure in the J/psi phi mass spectrum near threshold is observed in B-+/- -> J/psi phi K-+/- decays, produced in pp collisions at root 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 fb(-1). 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. (C) 2014 The Authors. Published by Elsevier B.V.