  We present a study of Bs0 decays to the CP-odd final state J/psi f0(980) with
J/psi -> mu+ mu- and f0(980) -> pi+ pi-. Using ppbar collision data with an
integrated luminosity of 3.8/fb collected by the CDF II detector at the
Tevatron we measure a Bs0 lifetime of tau(Bs0 -> J/psi f0(980)) = 1.70
-0.11+0.12(stat) +-0.03(syst) ps. This is the first measurement of the Bs0
lifetime in a decay to a CP eigenstate and corresponds in the standard model to
the lifetime of the heavy Bs0 eigenstate. We also measure the product of
branching fractions of Bs0 -> J/psi f0(980) and f0(980) -> pi+ pi- relative to
the product of branching fractions of Bs0 -> 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.
