The Ξc+ lifetime is measured using 9.0 fb-1 of e+e- annihilation data collected on and just below the Υ(4S) resonance with the CLEO II.V detector at CESR. This is the first measurement of the Ξc+ lifetime from a collider experiment. Using an unbinned maximum likelihood fit, the Ξc+ lifetime is measured to be 503 ±47(stat) ± 18(syst) fs. The precision of this measurement is comparable to previous measurements carried out by fixed target experiments with different sources of systematic uncertainties.