We have analyzed 116 fb^-1 of data collected by the BABAR detector for Xic0 production. In this paper we describe the observation of Xic0 production from ccbar continuum and from B decays, with the Xic0 decaying into (Xi- pi+) and (Omega- K+) modes. The ratio of the branching fractions of the Xic0 decays into these two final states measured in the ccbar continuum is: B(Xic0 -> Omega- K+) / B(Xic0 -> Xi- pi+) = 0.296 +- 0.018 (stat.) +- 0.030 (sys.). All results in this note are preliminary.