We report the first search for CP-violating decays of the Upsilon(4S) using a data sample that contains 535 x 10(6) Upsilon(4S) mesons with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. A partial reconstruction technique is employed to enhance the signal sensitivity. No significant signals were observed. We obtain an upper limit of 4 x 10(-7) at the 90% confidence level for the branching fractions of the CP violating modes, Upsilon(4S)-->B(0)B(0)-->J/psiK(S)(0)+J/psi(eta(c))K(S)(0). Extrapolating the result, we find that an observation with 5sigma significance is expected with a 30 ab(-1) data sample, which is within the reach of a future super B factory.