  Using $448.1\times 10 ^6$ $\psi(3686)$ decays collected with the BESIII
detector at the BEPCII $e^+e^-$ storage rings, the branching fractions and
angular distributions of the decays $\chi_{cJ}\to\Xi^-\bar{\Xi}^+$ and
$\Xi^0\bar{\Xi}^0$ $(J = 0, 1, 2)$ are measured based on a
partial-reconstruction technique. The decays $\chi_{c1}\to\Xi^0\bar{\Xi}^0$ and
$\chi_{c2}\to\Xi^0\bar{\Xi}^0$ are observed for the first time with statistical
significances of 7$\sigma$ and 15$\sigma$, respectively. The results of this
analysis are in good agreement with previous measurements and have
significantly improved precision.
