  This paper describes the measurement of elliptic flow of charged particles in
lead-lead collisions at sqrt(s_NN) = 2.76 TeV using the ATLAS detector at the
Large Hadron Collider (LHC). The results are based on an integrated luminosity
of approximately 7 ub^-1. Elliptic flow is measured over a wide region in
pseudorapidity, |eta| < 2.5, and over a broad range in transverse momentum, 0.5
< p_T < 20 GeV. The elliptic flow parameter v_2 is obtained by correlating
individual tracks with the event plane measured using energy deposited in the
forward calorimeters. As a function of transverse momentum, v_2(p_T) reaches a
maximum at p_T of about 3 GeV, then decreases and becomes weakly dependent on
p_T above 7 - 8 GeV. Over the measured pseudorapidity region, v_2 is found to
be approximately independent of |eta| for all collision centralities and
particle transverse momenta, something not observed in lower energy collisions.
The results are discussed in the context of previous measurements at lower
collision energies, as well as recent results from the LHC.
