Production of prompt J/ ψ meson pairs in proton-proton collisions at s 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 fb −1 . The two J/ ψ mesons are fully reconstructed via their decays into μ + μ − pairs. This observation provides for the first time access to the high-transverse-momentum region of J/ ψ 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/ ψ transverse momentum ( p T J/ ψ ) and rapidity (| y J/ ψ |): | y J/ ψ | < 1.2 for p T J/ ψ > 6.5 GeV/ c ; 1.2 < | y J/ ψ | < 1.43 for a p T threshold that scales linearly with | y J/ ψ | from 6.5 to 4.5 GeV/ c ; and 1.43 < | y J/ ψ | < 2.2 for p T J/ ψ > 4.5 GeV/ c . The total cross section, assuming unpolarized prompt J/ ψ pair production is 1.49 ± 0.07 (stat) ±0.13 (syst) nb. Different assumptions about ... mehr the J/ ψ polarization imply modifications to the cross section ranging from −31% to +27%.