  We present the first observation of the baryon decay
$\Lambda_b\to\Lambda_c\pi^-$ followed by $\Lambda_c\to p K^-\pi^+$ in 106 pb-1
of $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV in the CDF experiment. In
order to reduce systematic error, the measured rate for $\Lambda_b$ decay is
normalized to the kinematically similar meson decay $B^0\to D^+\pi^-$ followed
by $D^+\to\pi^+K^-\pi^+$. We report the ratio of production cross sections
($\sigma$) times the ratio of branching fractions (BR) for the momentum region
integrated above $p_T > 6$ GeV/c and pseudorapidity range $|\eta| < 1.3$:
$\sigma(p\bar{p}\to \Lambda_b X) / \sigma (p\bar{p}\to B^0 X) \times
BR(\Lambda_b\to\Lambda_c\pi^-) / BR(B^0\to D^+\pi^-) = 0.82 \pm 0.08(stat) \pm
0.11(syst) \pm 0.22 (BR(\Lambda_c\to p K^-\pi^+))$.
