  Using a $pp$ collision data sample corresponding to an integrated luminosity
of 3.0~fb$^{-1}$, collected by the LHCb detector, we present the first search
for the strangeness-changing weak decay $\Xi_b^-\to\Lambda_b^0\pi^-$. No $b$
hadron decay of this type has been seen before. A signal for this decay,
corresponding to a significance of 3.2 standard deviations, is reported. The
relative rate is measured to be
${{f_{\Xi_b^-}}\over{f_{\Lambda_b^0}}}{\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-) =
(5.7\pm1.8^{+0.8}_{-0.9})\times10^{-4}$, where $f_{\Xi_b^-}$ and
$f_{\Lambda_b^0}$ are the $b\to\Xi_b^-$ and $b\to\Lambda_b^0$ fragmentation
fractions, and ${\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-)$ is the branching
fraction. Assuming $f_{\Xi_b^-}/f_{\Lambda_b^0}$ is bounded between 0.1 and
0.3, the branching fraction ${\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-)$ would lie
in the range from $(0.57\pm0.21)\%$ to $(0.19\pm0.07)\%$.
