The tt¯ charge asymmetry is measured in events containing a charged lepton (electron or muon) and at least four jets, one of which is identified as originating from b-quark hadronization. The analyzed dataset corresponds to an integrated luminosity of 5.0 fb−1 collected with the CMS detector at the LHC. An inclusive and three differential measurements of the tt¯ charge asymmetry as a function of rapidity, transverse momentum, and invariant mass of the tt¯ system are presented. The measured inclusive tt¯ charge asymmetry is AC=0.004±0.010(stat.)±0.011(syst.). This result and the three differential measurements are consistent with zero asymmetry as well as with the predictions of the standard model.