  A search for the doubly charmed baryon $\Xi_{cc}^{+}$ is performed through
its decay to the $\Lambda_c^+ K^- \pi^+$ final state, using proton-proton
collision data collected with the LHCb detector at centre-of-mass energies of
7, 8 and 13$\mathrm{\,Te\kern -0.1em V}$. The data correspond to a total
integrated luminosity of $9\,\mathrm{fb}^{-1}$. No significant signal is
observed in the mass range from 3.4 to 3.8$\mathrm{\,Ge\kern -0.1em V}/c^2$.
Upper limits are set at $95\%$ credibility level on the ratio of the
$\Xi_{cc}^{+}$ production cross-section times the branching fraction to that of
$\Lambda_c^+$ and $\Xi_{cc}^{++}$ baryons. The limits are determined as
functions of the $\Xi_{cc}^{+}$ mass for different lifetime hypotheses, in the
rapidity range from 2.0 to 4.5 and the transverse momentum range from 4 to
15$\mathrm{\,Ge\kern -0.1em V}/c$.
