  We report a search for B -> J/psi D decays, based on a sample of 124 10^6
BBbar events collected with the BABAR detector at the PEP-II storage ring of
the Stanford Linear Accelerator Center. No significant signal is found. We
obtain upper limits on the branching fractions of 1.3 10^{-5} for B0 -> J/psi
D0bar and 1.2 10^{-4} for B+ -> J/psi D+ at 90% confidence level.
