  The decays $J/\psi\to\eta\Sigma^{+}\bar{\Sigma}{}^-$ and
$\psi(3686)\to\eta\Sigma^{+}\bar{\Sigma}{}^-$ are observed for the first time,
using $(10087 \pm 44)\times 10^{6}$ $J/\psi$ and $(448.1 \pm 2.9)\times 10^{6}$
$\psi(3686)$ events collected with the BESIII detector at the BEPCII collider.
We determine the branching fractions of these two decays to be ${\cal
B}(J/\psi\to\eta\Sigma^{+}\bar{\Sigma}{}^-)=(6.34 \pm 0.21 \pm 0.37)\times
10^{-5}$ and ${\cal B}(\psi(3686)\to\eta\Sigma^{+}\bar{\Sigma}{}^-)=(9.59 \pm
2.37 \pm 0.61)\times 10^{-6}$, where the first uncertainties are statistical
and the second are systematic. The ratio of these two branching fractions is
determined to be $\frac{{\cal
B}(\psi(3686)\to\eta\Sigma^{+}\bar{\Sigma}{}^-)}{{\cal
B}(J/\psi\to\eta\Sigma^{+}\bar{\Sigma}{}^-)}=(15.1 \pm 3.8)\%$, which is in
agreement with the "12\% rule."
