  The $\Xi_c^0$ baryon is unstable and usually decays into charmless final
states by the $c \to s u\overline{d}$ transition. It can, however, also
disintegrate into a $\pi^-$ meson and a $\Lambda_c^+$ baryon via $s$ quark
decay or via $cs\to d c$ weak scattering. The interplay between the latter two
processes governs the size of the branching fraction ${\cal{B}}$$(\Xi_c^0\to
\pi^-\Lambda_c^+)$, first measured here to be $(0.55\pm 0.02 \pm 0.18)$%, where
the first uncertainty is statistical and second systematic. This result is
compatible with the larger of the theoretical predictions that connect models
of hyperon decays using partially conserved axial currents and SU(3) symmetry
with those involving the heavy-quark expansion and heavy-quark symmetry. In
addition, the branching fraction of the normalization channel,
${\cal{B}}(\Xi_c^+\to p K^- \pi^+) = (1.135 \pm 0.002 \pm 0.387)$% is measured.
