  We study a possible origin of single spin asymmetries in the large $p_T$
inclusive production of hadrons in the scattering of unpolarized protons or
leptons on transversely polarized nucleons. Such asymmetry is related to the
single-spin asymmetry for the process $\p^\uparrow \to q+X$ or, equivalently,
to the off-diagonal matrix element of the quark density operator $\bar \psi
\gamma^+ \psi$; this quantity need not be zero if transverse momentum and
spin-isospin interactions are taken into account. The different signs for the
large single spin asymmetries observed in $\p^\uparrow p \to \pi^+ X$ and
$\p^\uparrow p \to \pi^- X$ can be explained as a consequence of chiral
symmetry. Crucial tests of the model are suggested.
