  A first search for $CP$ violation in the Cabibbo-suppressed
$\Xi_c^+\rightarrow pK^-\pi^+$ decay is performed using both a binned and an
unbinned model-independent technique in the Dalitz plot. The studies are based
on a sample of proton-proton collision data, corresponding to an integrated
luminosity of $3.0~{\rm fb^{-1}}$, and collected by the LHCb experiment at
centre-of-mass energies of $7$ and $8~\rm TeV$. The data are consistent with
the hypothesis of no $CP$ violation.
