  Recently, the Belle and LHCb Collaborations have measured the $\Lambda^+_c
\to p K^- \pi^+$ decay and reported the $p K^-$ invariant mass distribution,
which shows a clear cusp structure around the $\eta \Lambda$ threshold. In this
work, we have analyzed this process by considering the triangle mechanism and
the $S$-wave pseudoscalar meson-octet baryon interactions within the chiral
unitary approach, which dynamically generate the $\Lambda(1670)$. Our results
are in good agreement with the Belle measurements, which implies that the cusp
structure around $\eta\Lambda$ threshold could be associated with the
$\Lambda(1670)$ with the molecular nature.
