  Using an $e^+e^-$ collision data sample of $(27.08 \pm 0.14) \times 10^{8}$
$\psi(3686)$ events collected by the BESIII detector, we report the first
observation of $\chi_{cJ} \to \Omega^- \bar{\Omega}^+$ ($J=0,\,1,\,2$) decays
with significances of $5.6\sigma$, $6.4\sigma$, and $18\sigma$, respectively,
where the $\chi_{cJ}$ mesons are produced in the radiative $\psi(3686)$ decays.
The branching fractions are determined to be $\mathcal{B}(\chi_{c0} \to
\Omega^- \bar{\Omega}^+) = (3.51 \pm 0.54 \pm 0.29) \times 10^{-5}$,
$\mathcal{B}(\chi_{c1} \to \Omega^- \bar{\Omega}^+) = (1.49 \pm 0.23 \pm 0.10)
\times 10^{-5}$, and $\mathcal{B}(\chi_{c2} \to \Omega^- \bar{\Omega}^+) =
(4.52 \pm 0.24 \pm 0.18) \times 10^{-5}$, where the first and second
uncertainties are statistical and systematic, respectively.
