The standard model (SM) of particle physics is spectacularly successful, yet the measured value of the muon anomalous magnetic moment (g - 2)mu deviates from SM calculations by 3.6 sigma. Several theoretical models attribute this to the existence of a "dark photon," an additional U(1) gauge boson, which is weakly coupled to ordinary photons. The PHENIX experiment at the Relativistic Heavy Ion Collider has searched for a dark photon, U, in pi(0), eta -> gamma e(+)e(-) decays and obtained upper limits of O(2 x 10(-6)) on U-gamma mixing at 90% C.L. for the mass range 30 < m(U) < 90 MeV/c(2). Combined with other experimental limits, the remaining region in the U-gamma mixing parameter space that can explain the (g - 2)(mu) deviation from its SM value is nearly completely excluded at the 90% confidence level, with only a small region of 29 < m(U) < 32 MeV/c(2) remaining.