This Letter describes the measurement of elliptic flow of charged particles in lead–lead collisions at √sNN=2.76 TeV using the ATLAS detector at the Large Hadron Collider (LHC). The results are based on an integrated luminosity of approximately 7 μb−1. Elliptic flow is measured over a wide region in pseudorapidity, |η|<2.5|η|<2.5, and over a broad range in transverse momentum, 0.5<20 GeV. The elliptic flow parameter v2v2 is obtained by correlating individual tracks with the event plane measured using energy deposited in the forward calorimeters. As a function of transverse momentum, v2(pT) reaches a maximum at pT of about 3 GeV, then decreases and becomes weakly dependent on pT above 7–8 GeV. Over the measured pseudorapidity region, v2v2 is found to be only weakly dependent on η, with less variation than observed at lower beam energies. The results are discussed in the context of previous measurements at lower collision energies, as well as recent results from the LHC.