A search is presented for charge-asymmetric production of a W boson that has been proposed to accommodate the forward–backward asymmetry observed in the production of top–antitop quark pairs at the Tevatron. The new heavy W‘ boson would be produced in association with a top quark and would decay into top and down quarks. The data correspond to an integrated luminosity of 5.0 fb−1 in pp collisions at a center-of-mass energy of 7 TeV, recorded by the CMS detector at the LHC. No significant excess above the standard model expectations is observed, and, from a combination of the electron-plusjets and muon-plus-jets channels, a 95% confidence level lower limit of 840 GeV/c2 is set on the W‘ boson mass for a W‘ boson model with values for coupling constants to top and down quarks gL = 0 and gR = 2. In addition, a kinematic reconstruction of the W‘ resonance mass using the inherent charge asymmetry of this model finds no indication of the presence of W‘ events in the data.