The ratio of the Lambda(0)(b) baryon lifetime to that of the (B) over bar (0) meson is measured using 1.0 fb(-1) of integrated luminosity in 7 TeV center-of-mass energy pp collisions at the LHC. The Lambda(0)(b) baryon is observed for the first time in the decay mode Lambda(0)(b) -> J/psi pK(-), while the (B) over bar (0) meson decay used is the well known (B) over bar (0) J/psi pi K-+(-) mode, where the pi K-+(-) mass is consistent with that of the (K) over bar*(0)(892) meson. The ratio of lifetimes is measured to be 0.976 +/- 0: 012 +/- 0.006, in agreement with theoretical expectations based on the heavy quark expansion. Using previous determinations of the (B) over bar (0) meson lifetime, the Lambda(0)(b) lifetime is found to be 1.482 +/- 0.018 +/- 0.012 ps. In both cases, the first uncertainty is statistical and the second systematic.