A study of Bs0 → ηcϕ and Bs0 → ηcπ+π− 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 Bs0 → ηcϕ is reported, where the ηc meson is reconstructed in the pp¯ , K+K−π+π−, π+π−π+π− and K+K−K+K− decay modes and the ϕ(1020) in the K+K− decay mode. The decay Bs0 → J/ψϕ is used as a normalisation channel. Evidence is also reported for the decay Bs0 → ηcπ+π−, where the ηc meson is reconstructed in the pp¯ decay mode, using the decay Bs0 → J/ψπ+π− as a normalisation channel. The measured branching fractions are(Formula Presented.)where in each case the first uncertainty is statistical, the second systematic and the third uncertainty is due to the limited knowledge of the external branching fractions.[Figure not available: see fulltext.].