Abstract: A measurement of the lifetimes of the Omega(0)(c) and Xi(0)(c) baryons is reported using proton-proton collision data at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.4 fb(-1) collected by the LHCb experiment. The Omega(0)(c) and Xi(0)(c) baryons are produced directly from proton interactions and reconstructed in the pK(-)K(-)pi(+) final state. The Omega(0)(c) lifetime is measured to be 276.5 +/- 13.4 +/- 4.4 +/- 0.7 fs, and the Xi(0)(c) lifetime is measured to be 148.0 +/- 2.3 +/- 2.2 +/- 0.2 fs, where the first uncertainty is statistical, the second systematic, and the third due to the uncertainty on the D-0 lifetime. These results confirm previous LHCb measurements based on semileptonic beauty-hadron decays, which disagree with earlier results of a four times shorter Omega(c)0 lifetime, and provide the single most precise measurement of the Omega(0 )(c)lifetime.