The effective lifetime of the B ¯(s)(0) meson in the decay mode B¯(s)(0)→J/ψf(0)(980) is measured using 1.0 fb(-1) of data collected in pp collisions at √s=7 TeV with the LHCb detector. The result is 1.700±0.040±0.026 ps, where the first uncertainty is statistical and the second systematic. As the final state is CP-odd, and CP violation in this mode is measured to be small, the lifetime measurement can be translated into a measurement of the decay width of the heavy B¯(s)(0) mass eigenstate, Γ(H)=0.588±0.014±0.009 ps(-1).