We present a study of B-s(0) decays to the CP-odd final state J/psi f(0)(980) with J/psi -> mu(+)mu(-) and f(0)(980) -> pi(+)pi(-). Using p(p) over bar $ collision data with an integrated luminosity of 3.8 fb(-1) collected by the CDF II detector at the Tevatron we measure a B-s(0) lifetime of tau(B-s(0) -> J/psi f(0)(980)) = 1.70(-0.11)(+0.12)(stat) +/- 0.03(syst)ps. This is the first measurement of the B-s(0) lifetime in a decay to a CP eigenstate and corresponds in the standard model to the lifetime of the heavy B-s(0) eigenstate. We also measure the product of branching fractions of B-s(0) -> J/psi f(0)(980) and f(0)(980) -> pi(+)pi(-) relative to the product of branching fractions of B-s(0) -> J/psi phi and phi -> K+K- to be R-f0/phi = 0.257 +/- 0: 020(stat) +/- 0.014(syst), which is the most precise determination of this quantity to date. RI Prokoshin, Fedor/E-2795-2012