Using $(27.12\pm 0.14)\times {10}^8$ $\psi \left(3686\right)$ events collected with the BESIII detector, the decay ${\chi }_{c0}\to {\Sigma }^{+}{\overline{\Sigma }}^{-}\eta$ is observed for the first time with a signal significance of $7.0\sigma$, and evidence for ${\chi }_{c1}\to {\Sigma }^{+}{\overline{\Sigma }}^{-}\eta$ and ${\chi }_{c2}\to {\Sigma }^{+}{\overline{\Sigma }}^{-}\eta$ is found with signal significances of $4.3\sigma$ and $4.6\sigma$, respectively. The branching fractions are determined to be $B({\chi }_{c0}\to {\Sigma }^{+}{\overline{\Sigma }}^{-}\eta )=\left(1.26\pm 0.20\pm 0.13\right)\times {10}^{-4}$, $B({\chi }_{c1}\to {\Sigma }^{+}{\overline{\Sigma }}^{-}\eta )=\left(5.10\pm 1.21\pm 0.67\right)\times {10}^{-5}$, and $B({\chi }_{c2}\to {\Sigma }^{+}{\overline{\Sigma }}^{-}\eta )=\left(5.46\pm 1.18\pm 0.50\right)\times {10}^{-5}$, where the first uncertainties are statistical, and the second ones are systematic.