  The properties of baryons containing one heavy quark are studied in the
Skyrme model, where they are treated as bound states of a heavy meson with an
$SU(2)$ chiral soliton. In the large $N_c$ limit, the baryon spectrum is an
infinite tower of degenerate states with isospin and spin of the light degrees
of freedom $I=s_\ell=0,1,2,\dots$, and total spin $s=\abs{s_\ell\pm1/2}$.
Exotic states with no quark model analogues in the large $N_c$ limit are found
to be unbound. The $\Sigma_c-\Lambda_c$ mass difference is computed and found
to be in good agreement with experiment. The $\Sigma_c\,\Sigma_c\,\pi$ and
$\Sigma_c\,\Lambda_c\,\pi$ coupling constants are calculated to leading order
in $N_c$ in terms of $g_A$, the axial coupling constant of the nucleon. We
discuss the extension of our results to $SU(3)$ chiral solitons.
