Abstract: In the pp -> t (t) over bar 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 root 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 (m(t (t) over bar) > 0.75 TeV) and an absolute rapidity difference of the top and anti-top quark candidates within -2 vertical bar y(t)vertical bar – vertical bar y(<(t) over bar)vertical bar < 2is measured to be 4.2 +/- 3.2%, in agreement with the Standard Model prediction at next-to-leading order. A differential measurement in three <(t)over bar> mass bins is also presented.