  This paper presents the first measurement of event-by-event fluctuations of
the elliptic flow parameter v_2 in Au+Au collisions at sqrt(s_NN) = 200GeV as a
function of collision centrality. The relative non-statistical fluctuations of
the v_2 parameter are found to be approximately 40%. The results, including
contributions from event-by-event elliptic flow fluctuations and from azimuthal
correlations that are unrelated to the reaction plane (non-flow correlations),
establish an upper limit on the magnitude of underlying elliptic flow
fluctuations. This limit is consistent with predictions based on spatial
fluctuations of the participating nucleons in the initial nuclear overlap
region. These results provide important constraints on models of the initial
state and hydrodynamic evolution of relativistic heavy ion collisions.
