We report the results of the first search for B^{-} decays to the Ξ[over ¯]_{c}^{0}Λ[over ¯]_{c}^{-} final state using 711 fb^{-1} of data collected at the ϒ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e^{+}e^{-} collider. The results are interpreted in terms of both direct baryon-number-violating B^{-} decay and Ξ_{c}^{0}-Ξ[over ¯]_{c}^{0} oscillations which follow the standard model decay B^{-}→Ξ_{c}^{0}Λ[over ¯]_{c}^{-}. We observe no evidence for baryon number violation and set the 95% confidence-level upper limits on the ratio of baryon-number-violating and standard model branching fractions B(B^{-}→Ξ[over ¯]_{c}^{0}Λ[over ¯]_{c}^{-})/B(B^{-}→Ξ_{c}^{0}Λ[over ¯]_{c}^{-}) to be <2.7% and on the effective angular frequency of mixing ω in Ξ_{c}^{0}-Ξ[over ¯]_{c}^{0} oscillations to be <0.76 ps^{-1} (equivalent to τ_{mix}>1.3 ps).