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.  We use a sample with an integrated luminosity of \approx 90
pb^-1 recorded during the 1994-95 running period.  The decay vertices of
\approx 62656 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 ppbar collisions at sqrt s
= 1.8 TeV weighted by their branching ratios into J/psi, is 1.524 +/- 0.015
(stat)^+0.035_ -0.026 (sys) ps.  The precision of this measurement is
significantly improved compared to the inclusive lifetime measurement
published previously using \approx 10 pb^-1.