  An investigation of CP violation was performed using a total of 24 candidates
for B^0 -> J/psi K^0_S decay, with a purity of about 60%. These events were
selected from 4.4 million hadronic Z^0 decays recorded by the OPAL detector at
LEP. An analysis procedure, involving techniques to reconstruct the proper
decay times and tag the produced b-flavours, B^0 or B^0(bar), has been
developed to allow a first direct study of the time dependent CP asymmetry
that, in the Standard Model, is sin(2beta). The result is sin(2beta) =
3.2_{-2.0}^{+1.8} +/- 0.5, where the first error is statistical and the second
systematic. This result is used to determine probabilities for different values
of sin(2beta) in the physical region from -1 to +1.
