A first measurement of the polarization of W bosons with large transverse momenta in pp collisions is presented. The measurement is based on 36 pb⁻¹ of data recorded at √s = 7 TeV by the CMS detector at the LHC. The left-handed, right-handed, and longitudinal polarization fractions (f(L), f(R), and f₀, respectively) of W bosons with transverse momenta larger than 50 GeV are determined by using decays to both electrons and muons. The muon final state yields the most precise measurement: (f(L) - f(R))⁻ = 0.240 ± 0.036(stat) ± 0.031(syst) and f₀⁻ = 0.183 ± 0.087(stat) ± 0.123(syst) for negatively charged W bosons and (f(L) - f(R))⁺ = 0.310 ± 0.036(stat) ± 0.017(syst) and f₀⁺ = 0.171 ± 0.085(stat) ± 0.099(syst) for positively charged W bosons. This establishes, for the first time, that W bosons produced in pp collisions with large transverse momenta are predominantly left-handed, as expected in the standard model.