We report a measurement of the lifetime of the Ω{0/c} aryon 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 pK ⁻ 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 ± 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.