A measurement of the top-antitop (t (t) over bar) charge asymmetry is presented using data corresponding to an integrated luminosity of 4.6 fb(-1) of LHC pp collisions at a centre-of-mass energy of 7 TeV collected by the ATLAS detector. Events with two charged leptons, at least two jets and large missing transverse momentum are selected. Two observables are studied: A(C)(ll) based on the identified charged leptons, and A(C)(t (t) over bar), based on the reconstructed t (t) over bar final state. The asymmetries are measured to be A(C)(ll) =0.024 +/- 0.015 (stat.) +/- 0.009 (syst.), A(C)(t (t) over bar) = 0.021 +/- 0.025 (stat.) +/- 0.017 (syst.). The measured values are in agreement with the Standard Model predictions.