A search is presented for a massive particle, generically referred to as a Z′, decaying into a t-tbar pair. The search focuses on Z′ resonances that are sufficiently massive to produce highly Lorentz-boosted top quarks, which yield collimated decay products that are partially or fully merged into single jets. The analysis uses new methods to analyze jet substructure, providing suppression of the non-top multi-jet backgrounds. The analysis is based on a data sample of proton-proton collisions at a center-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 5 fb⁻¹ (inverse femtobarns). Upper limits in the range of 1 pb are set on the product of the production rates and branching fraction for a top-colour Z′ modelled for several widths, as well as for a Randall-Sundrum Kaluza-Klein gluon. In addition, any enhancement to t-tbar production for invariant masses above 1 TeV in the Standard Model is constrained.