Abstract: We report a measurement of the lifetime of the Omega(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 Omega(-)(b) -> Omega(0)(c)mu(-)nu X-mu signal decays, where the Omega(0)(c) baryon is detected in the pK(-)K(-)pi(+) thorn final state and X represents possible additional undetected particles in the decay. The Omega(0)(c) lifetime is measured to be tau(Omega c0) = 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.