Observation of the decays ${\chi }_{cJ}\to \varphi \varphi \eta$

Using a data sample of $(448.1\pm 2.9)\times {10}^6$ $\psi (3686)$ decays collected by the BESIII detector at the Beijing Electron Positron Collider (BEPCII), we observe the decays ${\chi }_{cJ}\to \varphi \varphi \eta (J=0,1,2)$, where the ${\chi }_{cJ}$ are produced via the radiative processes $\psi (3686)\to \gamma {\chi }_{cJ}$. The branching fractions are measured to be $\mathcal{B}({\chi }_{c0}\to \varphi \varphi \eta )=(8.41\pm 0.74\pm 0.62)\times {10}^{-4}$, $\mathcal{B}({\chi }_{c1}\to \varphi \varphi \eta )=(2.96\pm 0.43\pm 0.22)\times {10}^{-4}$, and $\mathcal{B}({\chi }_{c2}\to \varphi \varphi \eta )=(5.33\pm 0.52\pm 0.39)\times {10}^{-4}$, where the first uncertainties are statistical and the second are systematic. We also search for intermediate states in the $\varphi \varphi$ or $\eta \varphi$ combinations, but no significant structure is seen due to the limited statistics.