We report the observation of the baryonic B decay B̅ ^0→Λ_c^+Λ̅ K^- with a significance larger than 7 standard deviations based on 471×10^6 BB̅ pairs collected with the BABAR detector at the PEP-II storage ring at SLAC. We measure the branching fraction for the decay B̅ ^0→Λ_c^+Λ̅ K^- to be (3.8±0.8_(stat)±0.2_(sys)±1.0_(Λc)^+)×10^(-5). The uncertainties are statistical, systematic, and due to the uncertainty in the Λc+ branching fraction. We find that the Λ_c^+K^- invariant-mass distribution shows an enhancement above 3.5 GeV/c^2
