A search for resonant production of high-mass top-quark pairs is performed on 2.05 fb^-1 of proton-proton collisions at sqrt(s) = 7 TeV collected in 2011 with the ATLAS experiment at the Large Hadron Collider. This analysis of the lepton+jets final state is specifically designed for the particular topology that arises from the decay of highly boosted top quarks. The observed ttbar invariant mass spectrum is found to be compatible with the Standard Model prediction and 95% credibility level upper limits are derived on the ttbar production rate through new massive states. An upper limit of 0.7 pb is set on the production cross section times branching fraction of a narrow 1 TeV resonance. A Kaluza-Klein gluon with a mass smaller than 1.5 TeV is excluded.