We search for the doubly charmed baryonic decay B̄0→Λ c+Λ̄c-, in a data sample of 520×106 BB̄ events accumulated at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. We find no significant signal and set an upper limit of B(B̄0→Λc+Λ̄c-)<6.2×10-5 at 90% confidence level. The result is significantly below a naive extrapolation from B(B-→Ξc0Λ̄c-) assuming a simple Cabibbo-suppression factor of |Vcd/Vcs|2. The small branching fraction may be attributed to a suppression due to the large momentum of the baryonic decay products, which has been observed in other charmed baryonic two-body B decays. © 2008 The American Physical Society.