Abstract : We present a preliminary measurement of time-dependent CP-violating asymmetries in B0 -> J/psi K0S and B0 -> psi(2S) K0S decays recorded by the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. The data sample consists of 9.0 fb-1 collected at the Y(4S) resonance and 0.8 fb-1 off-resonance. One of the neutral B mesons, produced in pairs at the Y(4S), is fully reconstructed. The flavor of the other neutral B meson is tagged at the time of its decay, mainly with the charge of identified leptons and kaons. A neural network tagging algorithm is used to recover events without a clear lepton or kaon tag. The time difference between the decays is determined by measuring the distance between the decay vertices. Wrong-tag probabilities and the time resolution function are measured with samples of fully-reconstructed semileptonic and hadronic neutral B final states. The value of the asymmetry amplitude, sin2beta, is determined from a maximum likelihood fit to the time distribution of 120 tagged B0 -> J/psi K0S and B0 -> psi(2S) K0S candidates to be sin2beta = 0.12+/-0.37 (stat) +/- 0.09 (syst) (preliminary).