  We report first measurements of the doubly charmed baryonic B decays
B->Lambda_c+Lambda_c-K. The B+->Lambda_c+Lambda_c-K+ decay is observed with a
branching fraction of (6.5+1.0-0.9+-1.1+-3.4)x10^{-4} and a statistical
significance of 15.4sigma. The B0->Lambda_c+Lambda_c-K0 decay is observed with
a branching fraction of (7.9+2.9-2.3+-1.2+-4.2)x10^{-4} and a statistical
significance of 6.6sigma. The branching fraction errors are statistical,
systematic, and the error resulting from the uncertainty of Lambda_c+->pK-pi+
decay branching fraction. The analysis is based on 357fb-1 of data accumulated
at the Y(4S) resonance with the Belle detector at the KEKB asymmetric e+e-
collider.
