Observation of the decays chi(cJ) -> phi phi eta

Using a data sample of (448.1±2.9)×106 ψ(3686) decays collected by the BESIII detector at the Beijing Electron Positron Collider (BEPCII), we observe the decays χcJ→φφη(J=0,1,2), where the χcJ are produced via the radiative processes ψ(3686)→γχcJ. The branching fractions are measured to be B(χc0→φφη)=(8.41±0.74±0.62)×10-4, B(χc1→φφη)=(2.96±0.43±0.22)×10-4, and B(χc2→φφη)=(5.33±0.52±0.39)×10-4, where the first uncertainties are statistical, and the second are systematic. We also search for intermediate states in the φφ or ηφ subsystems, but no significant structure is seen due to the limited statistics.