  Using $(27.12\pm 0.14)\times10^{8}$ $\psi(3686)$ events collected with the
BESIII detector, we present the first observation of the decays
$\chi_{cJ}\to\Lambda\bar{\Lambda}\omega$, where $J=0, 1, 2$, with statistical
significances of $11.7 \sigma, 11.2 \sigma$, and $11.8 \sigma$. The branching
fractions of these decays are determined to be
$\mathcal{B}(\chi_{c0}\to\Lambda\bar{\Lambda}\omega)=({2.37 \pm 0.22 \pm 0.23})
\times 10^{-4}$, $\mathcal{B}(\chi_{c1}\to\Lambda\bar{\Lambda}\omega)=({1.01
\pm 0.10 \pm 0.11}) \times 10^{-4}$, and
$\mathcal{B}(\chi_{c2}\to\Lambda\bar{\Lambda}\omega)=({1.40 \pm 0.13 \pm 0.17})
\times 10^{-4}$, where the first uncertainties are statistical and the second
are systematic. We observe no clear intermediate structures.
