A search for resonant production of high-mass top-quark pairs is performed on 2.05 fb−1 of proton-proton collisions at 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 tt¯ invariant mass spectrum is found to be compatible with the Standard Model prediction and 95% credibility level upper limits are derived on the tt¯ 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.