We report the first measurement of charged particle elliptic flow in Pb–Pb collisions at √sNN = 2.76 TeV with the ALICE detector at the CERN Large Hadron Collider. The measurement is performed in the central pseudorapidity region (|η| < 0.8) and transverse momentum range 0.2 < pt < 5.0 GeV/c. The elliptic flow signal v2, measured using the 4-particle correlation method, averaged over transverse momentum and pseudorapidity is 0.087 ± 0.002 (stat) ± 0.004 (syst) in the 40–50% centrality class. The differential elliptic flow v2(pt) reaches a maximum of 0.2 near pt = 3 GeV/c. Compared to RHIC Au–Au collisions at √sNN = 200 GeV, the elliptic flow increases by about 30%. Some hydrodynamic model predictions which include viscous corrections are in agreement with the observed increase.