The t(t)Overbar charge asymmetry in proton-proton collisions root s = 7TeV is measured using the dilepton decay channel (ee, e mu, or mu mu). The data correspond to a total integrated luminosity of 5.0 fb(-1), collected by the CMS experiment at the LHC. The t(t) Overbar and lepton charge asymmetries, defined as the differences in absolute values of the rapidities between the reconstructed top quarks and antiquarks and of the pseudorapidities between the positive and negative leptons, respectively, are measured to be A(C) = -0.010 +/- 0.017 (stat.) +/- 0.008 (syst.) and A(C)(lep) = 0.009 +/- 0.010 (stat.) +/- 0.006 (syst.). The lepton charge asymmetry is also measured as a function of the invariant mass, rapidity, and transverse momentum of the system. All measurements are consistent with the expectations of the standard model.