The ratio of the Lambda b baryon lifetime to that of the B0 meson is measured using 1.0/fb of integrated luminosity in 7 TeV center-of-mass energy pp collisions at the LHC. The Lambda b baryon is observed for the first time in the decay mode Lambda b -> J/psi pK-, while the B0 meson decay used is the well known B0 -> J/psi pi+K- mode, where the pi+ 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 B0 meson lifetime, the Lambda 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.
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