We report a measurement of the lifetime of the Ω0c baryon using proton-proton collision data at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3.0  fb−1 collected by the LHCb experiment. The sample consists of about 1000  Ω−b→Ω0cμ−¯νμX signal decays, where the Ω0c baryon is detected in the pK−K−π+ final state and X represents possible additional undetected particles in the decay. The Ω0c lifetime is measured to be τΩ0c=268±24±10±2  fs, where the uncertainties are statistical, systematic, and from the uncertainty in the D+ lifetime, respectively. This value is nearly four times larger than, and inconsistent with, the current world-average value.