A study of B-s(0) -> eta(c)phi and B-s(0) -> eta(c)pi(+)pi(-) decays is performed using pp collision data corresponding to an integrated luminosity of 3.0 fb(-1), collected with the LHCb detector in Run 1 of the LHC. The observation of the decay B-s(0) -> eta(c)phi is reported, where the eta(c) meson is reconstructed in the p (p) over bar, K+K-pi(+)pi(-), pi(+)pi(-)pi(+)pi-and K+K-K+K-decay modes and the phi(1020) in the K+K-decay mode. The decay B-s(0) -> J/psi phi is used as a normalisation channel. Evidence is also reported for the decay B-s(0) -> eta(c)pi(+)pi(-), where the eta(c) meson is reconstructed in the p (p) over bar decay mode, using the decay B-s(0) -> J/psi phi pi(+)pi-as a normalisation channel. The measured branching fractions are B(B-s(0) -> eta(c)phi) = (5 : 01 +/- 0 : 53 +/- 0 : 27 +/- 0 : 63) x 10(-4), B(B-s(0) -> eta(c)pi(+)pi(-)) = (1 : 76 +/- 0 : 59 +/- 0 : 12 +/- 0 : 29) x 10(-4), where in each case the fi rst uncertainty is statistical, the second systematic and the third uncertainty is due to the limited knowledge of the external branching fractions.