  The recent measurements of azimuthal single spin asymmetries by the HERMES
collaboration has opened up new possibility to measure chiral-odd distribution
functions through semi-inclusive deep-inelastic scatterings. Here, predictions
are given for the twist-2 and twist-3 chiral-odd distribution functions of the
nucleon within the framework of the chiral quark soliton model, with full
inclusion of the vacuum polarization effects as well as the subleading $1/N_c$
corrections. The importance of the vacuum polarization effects is demonstrated
by showing that the so-called Soffer inequality holds not only for the quark
distributions but also for the antiquark ones.
