The first observation of the decays Λb0→χc1pK- and Λb0→χc2pK- is reported using a data sample corresponding to an integrated luminosity of 3.0 fb-1, collected by the LHCb experiment in pp collisions at center-of-mass energies of 7 and 8 TeV. The following ratios of branching fractions are measured: B(Λb0→χc1pK-)B(Λb0→J/ψpK-)=0.242±0.014±0.013±0.009,B(Λb0→χc2pK-)B(Λb0→J/ψpK-)=0.248±0.020±0.014±0.009,B(Λb0→χc2pK-)B(Λb0→χc1pK-)=1.02±0.10±0.02±0.05,where the first uncertainty is statistical, the second systematic, and the third due to the uncertainty on the branching fractions of the χc1→J/ψγ and χc2→J/ψγ decays. Using both decay modes, the mass of the Λb0 baryon is also measured to be mΛb0=5619.44±0.28±0.26 MeV/c2, where the first and second u...