The $\varLambda^0_b \to \varLambda^+_c K^+ K^- π^-$ 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 $\rm{TeV}$ collected by the $\mbox{LHCb}$ detector, corresponding to an integrated luminosity of $3{\rm{fb}^{-1}}$. The ratio of branching fractions between the $\varLambda^0_b \to \varLambda^+_c K^+ K^- π^-$ and the $\varLambda^{0}_{b}\to\varLambda^{+}_{c}D^{-}_{s}$ decays is measured to be \begin{equation*} \frac{\mathcal{B} ( \varLambda^0_b \to \varLambda^+_c K^+ K^- π^-) } {\mathcal{B} ( \varLambda^0_b \to \varLambda^+_c D^-_s)} = (9.26 \pm 0.29 \pm 0.46 \pm 0.26)\times10^{-2}, \end{equation*} where the first uncertainty is statistical, the second systematic and the third is due to the knowledge of the $D^-_s \to K^+ K^- π^-$ branching fraction. No structure on the invariant mass distribution of the $\varLambda^+_c K^+$ system is found, consistent with no open-charm pentaquark signature.