  The lowest moment of the twist-two, chiral-odd parton distribution $h_1(x)$
of the nucleon can be related to the so-called ``tensor charges'' of the
nucleon. We consider the tensor charges in the Skyrme model, and find that in
the large-$N_c$, SU(3)-symmetric limit, the model predicts that the octet
isosinglet tensor charge, $g^8_T$, is of order $1/N_c$ with respect to the
octet isovector tensor charge, $g^3_T$. The predicted $F/D$ ratio is then 1/3,
in the large-$N_c$ limit. These predictions coincide with the Skyrme model
predictions for the octet ${\it axial}$ charges, $g^8_A$ and $g^3_A$. (The
prediction $F/D=1/3$ for the axial charges differs from the commonly quoted
prediction of 5/9, which is based on an inconsistent treatment of the
large-$N_c$ limit.) The model also predicts that the singlet tensor charge,
$g^0_T$, is of order $1/N_c$ with respect to $g^3_T$.
