In the pp → tt ̄ process the angular distributions of top and anti-top quarks are expected to present a subtle difference, which could be enhanced by processes not included in the Standard Model. This Letter presents a measurement of the charge asymmetry in events where the top-quark pair is produced with a large invariant mass. The analysis is performed on 20.3 fb−1 of pp collision data at √s = 8 TeV collected by the ATLAS experiment at the LHC, using reconstruction techniques specifically designed for the decay topology of highly boosted top quarks. The charge asymmetry in a fiducial region with large invariant mass of the top-quark pair (mtt ̄ > 0.75 TeV) and an absolute rapidity difference of the top and anti-top quark candidates within −2 < |yt| − |yt ̄| < 2 is measured to be 4.2 ± 3.2%, in agreement with the Standard Model prediction at next-to-leading order. A differential measurement in three tt ̄ mass bins is also presented.