We present measurements of time-dependent CP-violating asymmetries in neutral B decays to several CP eigenstates. The measurement uses a data sample of 23 X 10(6) Y (4S) --> B (B) over bar decays collected by the BABAR detector at the PEP-II asymmetric B Factory at SLAG. Zn this sample, we find events in which one neutral B meson is fully reconstructed in a CP eigenstate containing charmonium and the flavor of the other neutral B meson is determined from its decay products. The amplitude of the CP-violating asymmetry, which in the standard model is proportional to sin2 beta, is derived from the decay time distributions in such events. The result is sin2 beta = 0.34 +/- 0.20 (stat) +/- 0.05 (syst).
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