  The difference between the $CP$ asymmetries in the decays $\varLambda_{c}^{+}
\to pK^{-}K^{+}$ and $\varLambda_{c}^{+} \to p\pi^{-}\pi^{+}$ is presented.
Proton-proton collision data taken at centre-of-mass energies of $7$ and
$8\,\mathrm{TeV}$ collected by the LHCb detector in 2011 and 2012 are used,
corresponding to an integrated luminosity of $3\,\mathrm{fb}^{-1}$. The
$\varLambda_{c}^{+}$ candidates are reconstructed as part of the
$\varLambda_{b}^{0} \to \varLambda_{c}^{+}\mu^{-}X$ decay chain. In order to
maximize the cancellation of production and detection asymmetries in the
difference, the final-state kinematic distributions of the two samples are
aligned by applying phase-space-dependent weights to the $\varLambda_{c}^{+}
\to p\pi^{-}\pi^{+}$ sample. This alters the definition of the integrated $CP$
asymmetry to $A_{CP}^{\text{wgt}}(p\pi^{-}\pi^{+})$. Both samples are corrected
for reconstruction and selection efficiencies across the five-dimensional
$\varLambda_{c}^{+}$ decay phase space. The difference in $CP$ asymmetries is
found to be \begin{align*}
  \Delta{A^{\text{wgt}}_{CP}} &= A_{CP}(pK^{-}K^{+}) -
A_{CP}^{\text{wgt}}(p\pi^{-}\pi^{+})\\
  &= (0.30 \pm 0.91 \pm 0.61)\,\%, \end{align*} where the first uncertainty is
statistical and the second is systematic.
