We present a measurement of the Bc+ meson lifetime in the decay mode Bc+ --> J/Psie+nue using the Collider Detector at Fermilab II detector at the Fermilab Tevatron Collider. From a sample of about of 360 pb(-1) of pp collisions at square root of s = 1.96 TeV, we reconstruct J/Psie+ pairs with invariant mass in the kinematically allowed range 4< M(J/Psie) < 6 GeV/c2. A fit to the decay-length distribution of 238 signal events yields a measured Bc+ meson lifetime of 0.463(-0.065)(+0.073)(stat) +/- 0.036(syst) ps.