A measurement of the mass difference between top and anti-top quarks is presented. In a 4.7 fb-1 data sample of proton--proton collisions at sqrt(s) = 7 TeV recorded with the ATLAS detector at the LHC, events consistent with ttbar production and decay into a single charged lepton final state are reconstructed. For each event, the mass difference between the top and anti-top quark candidate is calculated. A two b-tag requirement is used in order to reduce the background contribution. A maximum likelihood fit to these per-event mass differences yields mt-mtbar = 0.67 +/- 0.61 (stat) +/- 0.41 (syst) GeV, consistent with CPT invariance.