Production of prompt J/ψ 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 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 the J/ψ polarization imply modifications to the cross section ranging from −31% to +27%.