The average b-hadron lifetime has been measured using a high
statistics sample of B -> J/psi X decays recorded with the Collider
Detector at Fermilab.  The decay vertices of 5344 inclusive J/psi -> mu+ mu-
candidates have been reconstructed using information from a silicon
vertex detector.  The measured B lifetime, which is the average over all
b-hadrons produced in p p-bar collisions at sqrt{s} = 1.8 TeV
weighted by their branching ratios into J/psi, is
1.46 +- 0.06(stat) +- 0.06(sys) ps.