We report a measurement of the lifetime of the Ω 0 c 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 → Ω 0 c μ − ¯ ν μ X signal decays, where the Ω 0 c baryon is detected in the p K − K − π + final state and X represents possible additional undetected particles in the decay. The Ω 0 c lifetime is measured to be τ Ω 0 c = 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.