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-plus-jets and muon-plus-jets channels, a 95% confidence level lower limit of 840 GeV / c 2 is set on the W ' boson mass for a W ' boson model with values for coupling constants to top and down quarks g L = 0 and g R = 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.