Measurements of the top-antitop quark pair production charge asymmetry in the dilepton channel, characterized by two high-pT leptons (electrons or muons), are presented using data corresponding to an integrated luminosity of 20.3 fb−1 from pp collisions at a center-of-mass energy √s=8 TeV collected with the ATLAS detector at the Large Hadron Collider at CERN. Inclusive and differential measurements as a function of the invariant mass, transverse momentum, and longitudinal boost of the tt¯ system are performed both in the full phase space and in a fiducial phase space closely matching the detector acceptance. Two observables are studied: AℓℓC based on the selected leptons and Att¯C based on the reconstructed tt¯ final state. The inclusive asymmetries are measured in the full phase space to be AℓℓC=0.008±0.006 and Att¯C=0.021±0.016, which are in agreement with the Standard Model predictions of AℓℓC=0.0064±0.0003 and Att¯C=0.0111±0.0004.