The lifetime of the B0 s meson is measured in the decay channel B0 s → J=ψπþπ− with 880 ≤ Mπþπ− ≤ 1080 MeV=c2, which is mainly a CP-odd state and dominated by the f0ð980Þ resonance. In 10.4 fb−1 of data collected with the D0 detector in Run II of the Tevatron, the lifetime of the B0 s meson is measured to be τ(B0 s) = 1.70 0.14(stat) 0.05(syst) ps. Neglecting CP violation in B0 s=B¯ 0 s mixing, the measurement can be translated into the width of the heavy mass eigenstate of the B0 s, ΓH = 0.59 +- 0.05(stat) 0.02(syst) ps−1.