  By analyzing $(448.1\pm2.9)\times10^6$ $\psi(3686)$ events collected with the
BESIII detector operating at the BEPCII collider, the decays of $\chi_{cJ} \to
\Lambda\bar \Lambda \eta$ ($J=0$, 1 and 2) are observed for the first time with
statistical significances of $13.9\sigma$, $6.7\sigma$, and $8.2\sigma$,
respectively. The product branching fractions of $\psi(3686)\to\gamma\chi_{cJ}$
and $\chi_{cJ}\to \Lambda\bar \Lambda \eta$ are measured. Dividing by the world
averages of the branching fractions of $\psi(3686)\to\gamma\chi_{cJ}$, the
branching fractions of $\chi_{cJ}\to \Lambda\bar \Lambda \eta$ decays are
determined to be $(2.31\pm0.30\pm0.21)\times10^{-4}$,
$(5.86\pm1.38\pm0.68)\times10^{-5}$, and $(1.05\pm0.21\pm0.15)\times10^{-4}$
for $J=0$, 1 and 2, respectively, where the first uncertainties are statistical
and the second systematic.
