  Using the data sample of 711 fb$^{-1}$ of $\Upsilon(4S)$ on-resonance data
taken by the Belle detector at the KEKB asymmetric-energy electron-positron
collider, we present the first measurements of branching fractions of the
decays $B^{-} \to \bar{\Lambda}_{c}^{-} \Xi_{c}^{'0}$, $B^{-} \to
\bar{\Lambda}_{c}^{-} \Xi_{c}(2645)^{0}$, and $B^{-} \to \bar{\Lambda}_{c}^{-}
\Xi_{c}(2790)^{0} $. The signal yields for these decays are extracted from the
recoil mass spectrum of the system recoiling against $\bar{\Lambda}_{c}^{-}$
baryons in selected $B^-$ candidates. The branching fraction of $B^{-} \to
\bar{\Lambda}_{c}^{-} \Xi_{c}(2790)^{0}$ is measured to be $ (1.1 \pm 0.4 \pm
0.2)\times 10^{-3}$, where the first uncertainty is statistical and the second
systematic. The 90\% credibility level upper limits on ${\cal B}(B^{-} \to
\bar{\Lambda}_{c}^{-} \Xi_{c}^{'0})$ and ${\cal B}(B^{-} \to
\bar{\Lambda}_{c}^{-} \Xi_{c}(2645)^{0})$ are determined to be $6.5\times
10^{-4}$ and $7.9\times 10^{-4}$, respectively.
