This paper reports inclusive and differential measurements of the tt¯ charge asymmetry AC in 20.3 fb−1 of √s=8 TeV pp collisions recorded by the ATLAS experiment at the Large Hadron Collider at CERN. Three differential measurements are performed as a function of the invariant mass, transverse momentum and longitudinal boost of the tt¯ system. The tt¯ pairs are selected in the single-lepton channels (e or μ) with at least four jets, and a likelihood fit is used to reconstruct the tt¯ event kinematics. A Bayesian unfolding procedure is performed to infer the asymmetry at parton level from the observed data distribution. The inclusive tt¯ charge asymmetry is measured to be AC=0.009±0.005 (stat. + syst.). The inclusive and differential measurements are compatible with the values predicted by the Standard Model.