The effective lifetime of the (B) over bar (0)(s) meson in the decay mode (B) over bar (0)(s) -> J / psi f(0)(980) is measured using 1.0 fb(-1) of data collected in p p collisions at root 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) over bar (0)(s) mass eigenstate, Gamma(H) = 0.588 +/- 0.014 +/- 0.009 ps(-1).