Production of prompt J/Ψ  meson pairs in proton-proton collisions at √s =7TeV 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 (pT^J/Ψ ) and rapidity (|y^J/Ψ |): |y^J/Ψ | < 1.2 for p^J/Ψ _T > 6.5 GeV/c; 1.2 < |y^J/Ψ | < 1.43 for a pT 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^J/Ψ T > 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 the J/Ψ  polarization imply modifications to the cross section ranging from −31% to +27%.