  We study a bino-like light neutralino ($\tilde \chi_1^0$) produced at the LHC
from the decay of a scalar lepton ($\tilde e_L$) through the process $pp\to
\tilde e_{L} \to e\tilde \chi_1^0$ in the context of R-parity-violating (RPV)
supersymmetry where $\tilde \chi_1^0$ is the lightest supersymmetric particle.
For small masses and RPV couplings, the neutralino is naturally long-lived and
its decay products can be identified as displaced tracks. Following existing
searches, we propose a displaced-vertex search strategy for such a light
neutralino with a single RPV coupling switched on, $\lambda'_{111}$, in the
mass range $10\,\mbox{GeV} \lesssim m_{\tilde \chi_1^0}\lesssim
230\,\mbox{GeV}$. We perform Monte Carlo simulations and conclude that at the
high-luminosity LHC, the proposed search can probe values of $\lambda'_{111}$
down to two orders of magnitude smaller than current bounds and up to 40 times
stronger than projected limits from monolepton searches.
