  Using $(448.1 \pm 2.9) \times 10^{6}$ $\psi(3686)$ events collected with the
BESIII detector, we perform the first search for the weak baryonic decay
$\psi(3686) \to \Lambda_c^{+} \bar{\Sigma}^- +c.c.$. The analysis procedure is
optimized using a blinded method. No significant signal is observed, and the
upper limit on the branching fraction ($\mathcal B$) of $\psi(3686) \to
\Lambda_c^{+} \bar{\Sigma}^- +c.c.$ is set to be $1.4\times 10^{-5}$ at the
90\% confidence level.
