We report a measurement of the lifetime of the Ω_{c}^{0} 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_{c}^{0}μ^{-}ν[over ¯]_{μ}X signal decays, where the Ω_{c}^{0} baryon is detected in the pK^{-}K^{-}π^{+} final state and X represents possible additional undetected particles in the decay. The Ω_{c}^{0} lifetime is measured to be τ_{Ω_{c}^{0}}=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.