Using a $pp$ collision data sample corresponding to an integrated luminosity of $3.0\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, collected by the LHCb detector, we present the first search for the strangeness-changing weak decay ${\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{b}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}$. No $b$ hadron decay of this type has been seen before. A signal for this decay, corresponding to a significance of 3.2 standard deviations, is reported. The relative rate is measured to be $\frac{{f}_{{\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}}}{{f}_{{\mathrm{\ensuremath{\Lambda}}}_{b}^{0}}}\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{b}^{0}{\ensuremath{\pi}}^{\ensuremath{-}})=(5.7\ifmmode\pm\else\textpm\fi{}1.{8}_{\ensuremath{-}0.9}^{+0.8})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4},$where ${f}_{{\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}}$ and ${f}_{{\mathrm{\ensuremath{\Lambda}}}_{b}^{0}}$ are the $b\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}$ and $b\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{b}^{0}$ fragmentation fractions, and $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{b}^{0}{\ensuremath{\pi}}^{\ensuremath{-}})$ is the branching fraction. Assuming ${f}_{{\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}}/{f}_{{\mathrm{\ensuremath{\Lambda}}}_{b}^{0}}$ is bounded between 0.1 and 0.3, the branching fraction $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{b}^{0}{\ensuremath{\pi}}^{\ensuremath{-}})$ would lie in the range from $(0.57\ifmmode\pm\else\textpm\fi{}0.21)%$ to $(0.19\ifmmode\pm\else\textpm\fi{}0.07)%$.