An investigation of CP violation was performed using a total of 24 candidates for B0→J/ψK0SB0→J/ψKS0 decay, with a purity of about 60%. These events were selected from 4.4 million hadronic Z0Z0 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, B0B0 or B¯0B¯0 , has been developed to allow a first direct study of the time dependent CP asymmetry that, in the Standard Model, is sin2βsin⁡2β . The result is where the first error is statistical and the second systematic. This result is used to determine probabilities for different values of sin2βsin⁡2β in the physical region from −1−1 to +1.