Using data collected in the region of the $\Upsilon(4S)$ resonance with the CLEO-II detector, the first observation of exclusive decays of the B meson to final states with a charmed baryon is reported which is essential in understanding the mechanism for baryon production from the weak decays of the B-meson. We have measured the branching fractions to be ${\cal B}(\bar B\sp-\to\Lambda\sbsp{c}{+}\bar p\pi\sp-)=(0.62\sbsp{-0.20}{+0.23}\pm 0.11\pm0.10)\times10\sp{-3}$ and ${\cal B}(\bar B\sp0\to\Lambda\sbsp{c}{+}\bar p\pi\sp+\pi\sp-)=(1.33\sbsp{-0.42}{+0.46}\pm0.31\pm0.21)\times10 \sp{-3}.$ In addition, we report upper limits for the final states $\bar B\sp0\to\Lambda\sbsp{c}{+}\bar p$ and $B\sp-\to\Lambda\sbsp{c}{+}\bar p\pi\sp+\pi\sp-.$ The two-body decay, $\bar B\sp0\to\Lambda\sbsp{c}{+}\bar p,$ is suppressed in disagreement with theoretical predictions.