The Lambda+c lifetime is measured using 9.0 fb(-1) of e+e- annihilation data collected on or just below the Upsilon(4S) resonance with the CLEO II.V detector at CESR. Using an unbinned maximum likelihood fit, the Lambda+c lifetime is measured to be 179.6+/-6.9(stat)+/-4.4(syst) fs. The precision of this colliding beam measurement is comparable to other measurements, which are based on fixed-target experiments, with different systematic uncertainties.