We report the first direct observation of the strange $b$ baryon ${\ensuremath{\Xi}}_{b}^{\ensuremath{-}}({\overline{\ensuremath{\Xi}}}_{b}^{+})$. We reconstruct the decay ${\ensuremath{\Xi}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\Xi}}^{\ensuremath{-}}$, with $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, and ${\ensuremath{\Xi}}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\Lambda}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ in $p\overline{p}$ collisions at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$. Using $1.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data collected by the D0 detector, we observe $15.2\ifmmode\pm\else\textpm\fi{}4.4(\mathrm{stat}{)}_{\ensuremath{-}0.4}^{+1.9}(\mathrm{syst})$ ${\ensuremath{\Xi}}_{b}^{\ensuremath{-}}$ candidates at a mass of $5.774\ifmmode\pm\else\textpm\fi{}0.011(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.015(\mathrm{syst})\text{ }\text{ }\mathrm{GeV}$. The significance of the observed signal is $5.5\ensuremath{\sigma}$, equivalent to a probability of $3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ of it arising from a background fluctuation. Normalizing to the decay ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\Lambda}$, we measure the relative rate $\frac{\ensuremath{\sigma}({\ensuremath{\Xi}}_{b}^{\ensuremath{-}})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({\ensuremath{\Xi}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\Xi}}^{\ensuremath{-}})}{\ensuremath{\sigma}({\ensuremath{\Lambda}}_{b})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\Lambda})}=0.28\ifmmode\pm\else\textpm\fi{}0.09(\mathrm{stat}{)}_{\ensuremath{-}0.08}^{+0.09}(\mathrm{syst})$.