Two-particle azimuthal correlation functions are presented for charged hadrons produced in Au + Au collisions at the Relativistic Heavy Ion Collider (roots(NN) = 130 GeV). The measurements permit determination of elliptic flow without event-by-event estimation of the reaction plane. The extracted elliptic flow values (upsilon(2)) show significant sensitivity to both the collision centrality and the transverse momenta of emitted hadrons, suggesting rapid thermalization and relatively strong velocity fields. When scaled by the eccentricity of the collision zone epsilon, the scaled elliptic flow shows little or no dependence on centrality for charged hadrons with relatively low p(T). A breakdown of this epsilon scaling is observed for charged hadrons with p(T) > 1.0 GeV/c.