  We report the first observation of the decay B+ -> \bar{\Xi}_c^0 \Lambda_c^+
with a significance of 8.7 \sigma and evidence for the decay B^0 ->
\bar{\Xi}_c^-\Lambda_c^+ with a significance of 3.8 \sigma. The product Br(B^+
-> \bar{\Xi}_c^0\Lambda_c^+)\times Br(\bar{\Xi}_c^0 -> \bar{\Xi}^+\pi^-) is
measured to be (4.8^{+1.0}_{-0.9}\pm 1.1\pm 1.2)\times 10^{-5}, and Br({B^0} ->
\bar{\Xi}_c^-\Lambda_c^+)\times Br(\bar{\Xi}_c^- -> \bar{\Xi}^+\pi^-\pi^-) is
measured to be (9.3^{+3.7}_{-2.8}\pm 1.9\pm 2.4)\times 10^{-5}. The errors are
statistical, systematic and the error of the \Lambda_c^+ -> pK^-\pi^+ branching
fraction, respectively. The decay B^+ -> \bar{\Xi}_c^0\Lambda_c^+ is the first
example of a two-body exclusive B^+ decay into two charmed baryons. The data
used for this analysis was accumulated at the \Upsilon(4S) resonance, using the
Belle detector at the e^+ e^- asymmetric-energy collider KEKB. The integrated
luminosity of the data sample is equal to 357 {fb}^{-1}, corresponding to
386\times 10^{6} B{\bar B} pairs.
