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 root s = 7 TeV by the CMS detector at the LHC. The left-handed, right-handed, and longitudinal polarization fractions (f(L), f(R), and f(0), 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(syst) +/- 0.031(syst) and f(0)(-) = 0.183 +/- 0.087(stat) +/- 0.123(syst) for negatively charged W bosons and (f(L) - f(R))(+) = 0.310 +/- 0.036(syst) +/- 0.017(syst) and f(0)(+) = 0.171 +/- 0.085(syst) +/- 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.