The ${\Lambda }_b^0\to {\Lambda }_c^{+}{K}^{+}{K}^{-}{\pi }^{-}$ decay is observed for the first time using a data sample of proton-proton collisions at centre-of-mass energies of $\sqrt{s}=7$ and $8\text{TeV}$ collected by the LHCb detector, corresponding to an integrated luminosity of $3f{b}^{-1}$. The ratio of branching fractions between the ${\Lambda }_b^0\to {\Lambda }_c^{+}{K}^{+}{K}^{-}{\pi }^{-}$ and the ${\Lambda }_b^0\to {\Lambda }_c^{+}{D}_s^{-}$ decays is measured to be$\frac{B({\Lambda }_b^0\to {\Lambda }_c^{+}{K}^{+}{K}^{-}{\pi }^{-})}{B({\Lambda }_b^0\to {\Lambda }_c^{+}{D}_s^{-})}=(9.26\pm 0.29\pm 0.46\pm 0.26)\times {10}^{-2},$ where the first uncertainty is statistical, the second systematic and the third is due to the knowledge of the $D_s^{-}\to K^{+}{K}^{-}{\pi }^{-}$ branching fraction. No structure on the invariant mass distribution of the ${\Lambda }_c^{+}{K}^{+}$ system is found, consistent with no open-charm pentaquark signature.