A measurement of the correlations between the polar angles of leptons from the decay of pair-produced t and (t) over bar quarks in the helicity basis is reported, using proton-proton collision data collected by the ATLAS detector at the LHC. The dataset corresponds to an integrated luminosity of 4.6 fb(-1) at a center-of-mass energy of root s = 7 TeV collected during 2011. Candidate events are selected in the dilepton topology with large missing transverse momentum and at least two jets. The angles theta(1) and theta(2) between the charged leptons and the direction of motion of the parent quarks in the t (t) over bar rest frame are sensitive to the spin information, and the distribution of cos theta(1).cos theta(2) is sensitive to the spin correlation between the t and (t) over bar quarks. The distribution is unfolded to parton level and compared to the next-to-leading order prediction. A good agreement is observed.