  We present a preliminary measurement of time-dependent CP-violating
asymmetries in B^0-->J/psi K_S and B^0-->psi(2S) K_S decays recorded by the
BABAR detector at the PEP-II asymmetric B Factory at SLAC. The data sample
consists of 9.0 fb-1 collected at the Upsilon(4S) resonance and 0.8 fb-1
off-resonance. One of the neutral B mesons, produced in pairs at the
Upsilon(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. 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, sin(2*beta), is determined from a maximum likelihood fit to the time
distribution of 120 tagged B^0-->J/psi K_S and B^0-->psi(2S) K_S candidates:
sin(2*beta) = 0.12+/-0.37(stat)+/-0.09(syst).
