The average b-hadron lifetime has been measured using a high statistics sample of[ital B][r-arrow][ital J]/[psi][Chi] decays recorded with the Collider Detector at Fermilab. We use a sample with an integrated luminosity of[approx] 90[ital pb][sup -1] recorded during the 1994-95 running period. The decay vertices of[approx] 62656 inclusive[ital J]/[psi][r-arrow][mu][sup+][mu][sup -] candidates have been reconstructed using information from a silicon vertex-detector. The measured[ital B]lifetime, which is the average over all b-hadrons produced in[ital p][ital[anti p]] collisions at[radical]s= 1.8 TeV weighted by their branching ratios into[ital J]/[psi], is 1.524[+-] 0.015 ([ital stat])[sup+0.035][sub -0.026] ([ital sys]) ps. The precision of this measurement is significantly improved compared to the inclusive lifetime measurement published previously using[approx] 10[ital pb][sup -1].