  Using a data sample of $(448.1\pm2.9)\times 10^6~\psi(3686)$ events collected
with the BESIII detector at the BEPCII collider, we present measurements of
branching fractions for the decays $\chi_{cJ} \rightarrow \Sigma^+
\bar{\Sigma}^-$ and $\Sigma^0 \bar{\Sigma}^0$. The decays
$\chi_{c1,2}\rightarrow \Sigma^+ \bar{\Sigma}^-$ and $\Sigma^0 \bar{\Sigma}^0$
are observed for the first time, and the branching fractions for
$\chi_{c0}\rightarrow \Sigma^+ \bar{\Sigma}^-$ and $\Sigma^0 \bar{\Sigma}^0$
decays are measured with improved precision. The branching fraction ratios
between the charged and neutral modes are consistent with the prediction of
isospin symmetry.
