We report the observation of the baryonic decay B¯0→Λc+p¯K-K+ using a data sample of 471×106 BB¯ pairs produced in e+e- annihilations at s=10.58GeV. This data sample was recorded with the BABAR detector at the PEP-II storage ring at SLAC. We find B(B¯0→Λc+p¯K-K+)=(2.5±0.4(stat)±0.2(syst)±0.6B(Λc+))×10-5, where the uncertainties are statistical, systematic, and due to the uncertainty of the Λc+→pK-π+ branching fraction, respectively. The result has a significance corresponding to 5.0 standard deviations, including all uncertainties. For the resonant decay B¯0→Λc+p¯φ, we determine the upper limit B(B¯0→Λc+p¯φ)<1.2×10-5 at 90% confidence level.