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