Production of prompt J/$\psi$ meson pairs in proton-proton collisions at $\sqrt{s}$ = 7 TeV is measured with the CMS experiment at the LHC in a data sample corresponding to an integrated luminosity of about 4.7 inverse-femtobarns. The two J/$\psi$ mesons are fully reconstructed via their decays into $\mu^+\mu^-$ pairs. This observation provides for the first time access to the high-transverse-momentum region of J/$\psi$ pair production where model predictions are not yet established. The total and differential cross sections are measured in a phase space defined by the individual J/$\psi$ transverse momentum ($p_T^{J/\psi}$) and rapidity (|$y^{J/\psi}$|): |$y^{J/\psi}$| lower than 1.2 for $p_T^{J/\psi}$ greater than 6.5 GeV/c; |$y^{J/\psi}$| in [1.2,1.43] for a $p_T$ threshold that scales linearly with |$y^{J/\psi}$| from 6.5 to 4.5 GeV/c; and |$y^{J/\psi}$| in [1.43,2.2] for $p_T^{J/\psi}$ greater than 4.5 GeV/c. The total cross section, assuming unpolarized prompt J/$\psi$ pair production is 1.49 $\pm$ 0.07 (stat.) $\pm$ 0.13 (syst.) nb. Different assumptions about the J/$\psi$ polarization imply modifications to the cross section ranging from -31% to +27%.
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