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Using the CLEO-II data set we have searched for the decays B0 → D(*)+D(*)-. We observe one candidate signal event for the decay B0 → D*+D*- with an expected background of 0.022 ± 0.011 events. This yield corresponds to a branching fraction of B(B0 → D*+D*-) = [5.317-3.7+7.1(stat) ± 1.0(syst)] x 10-4 and an upper limit of B(B0 → D*+D*-) < 2.2 X 10-3 at the 90% C.L. We see no significant excess of signal above the expected background level in the other modes, and we calculate the 90% C.L. upper limits on the branching fractions to be B(B0 → D*±D±) < 1.8 X 10-3 and B(B0 → D+D-) < 1.2 X 10-3.