A measurement of the top-antitop production charge asymmetry A_C is presented using data corresponding to an integrated luminosity of 1.04 fb^-1 of pp collisions at sqrt(s) = 7 TeV collected by the ATLAS detector at the LHC. Events are selected with a single lepton (electron or muon), missing transverse momentum and at least four jets of which at least one jet is identified as coming from a b-quark. A kinematic fit is used to reconstruct the ttbar event topology. After background subtraction, a Bayesian unfolding procedure is performed to correct for acceptance and detector effects. The measured value of A_C is A_C = -0.018 +/- 0.028 (stat.) +/- 0.023 (syst.), consistent with the prediction from the MC@NLO Monte Carlo generator of A_C = 0.006 +/- 0.002. Measurements of A_C in two ranges of invariant mass of the top-antitop pair is also shown.