The ratio of the Λb(0) baryon lifetime to that of the B(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 Λb(0) baryon is observed for the first time in the decay mode Λb(0)→J/ψpK-, while the B(0) meson decay used is the well known B(0)→J/ψπ+ K- mode, where the π+ K- mass is consistent with that of the K(*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(0) meson lifetime, the Λb(0) lifetime is found to be 1.482±0.018±0.012 ps. In both cases, the first uncertainty is statistical and the second systematic.