Using data collected with the LHCb detector in proton-proton collisions at a centre-of-mass energy of 7 TeV, the hadronic decay B-s(0) -> J/psi f(0)(980) is observed. This CP eigenstate mode could be used to measure mixing-induced CP violation in the B? system. Using a fit to the pi(+)pi(-) mass spectrum with interfering resonances gives R-f0/phi equivalent to inverted right perpendicular(B-s(0) -> J/psi f(0) -> pi(+)pi(-)/inverted right perpendicular(B-s(0) -> J/psi phi,phi -> K+K-) = 0.252(-0.032-0.033)(+0.046+0.027). In the interval +/- 90 MeV around 980 MeV, corresponding to approximately two full Jo widths we also find R' equivalent to inverted right perpendicular(B-s(0) -> J/psi pi(+)pi(-),vertical bar m(pi(+)pi(-))-980 MeV vertical bar<90 MeV)/inverted right perpendicular(B-s(0) -> J/psi phi,phi -> K+K- = 0.162 +/- 0.022 +/- 0.016, where in both cases the uncertainties are statistical and systematic, respectively. (C) 2011 CERN. Published by Elsevier B.V. All rights reserved.