We present a study of B0
decays to the CP-odd final state J/f0(980) with ?and
f0(980) ?0. Using p? collision data with an integrated luminosity of 3.8 fb?01 collected by the
CDF II detector at the Tevatron we measure a B0
s lifetime of B0
s J f0(980)) = 1.70+0.12
?60.11(stat)0.03(syst) ps. This is the first measurement of the B0
s lifetime in a decay to a CP eigenstate and
corresponds in the standard model to the lifetime of the heavy B0
s eigenstate.