The FOCUS experiment(FNAL-E831) has used two channels, $Omega^- pi^+$ and $Xi^-K^- pi^+ pi^+$,to measure the lifetime of the $Omega_c^0$ charmed baryon. From a sample of $64 pm 14$ signal events at a mass of 2.698 GeV/$c^2$, we measure an $Omega_c^0$ lifetime of $72 pm 11$ (stat.) $pm 11$ (sys.) fs, substantially improving upon the current world average.