We report the first measurements of the doubly charmed baryonic B decays B→Λc+Λc-K. The B+→Λc+Λc-K+ decay is observed with a branching fraction of (6.5-0.9+1.0±1.1±3.4) ×10-4 and a statistical significance of 15.4σ. The B0→Λc+Λc-K0 decay is observed with a branching fraction of (7.9-2.3+2.9±1.2±4.1)×10-4 and a statistical significance of 6.6σ. The branching fraction errors are statistical, systematic, and the error resulting from the uncertainty of the Λc+→pK-π+ decay branching fraction. The analysis is based on 357fb-1 of data accumulated at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider.