  Using SU(3) chiral perturbation theory we calculate the density-dependent
complex-valued spin-orbit coupling strength $U_{\Sigma ls}(k_f)+ i W_{\Sigma
ls}(k_f)$ of a $\Sigma$ hyperon in the nuclear medium. The leading long-range
$\Sigma N$ interaction arises from iterated one-pion exchange with a $\Lambda$
or a $\Sigma$ hyperon in the intermediate state. We find from this unique
long-range dynamics a sizeable ``wrong-sign'' spin-orbit coupling strength of
$U_{\Sigma ls}(k_{f0}) \simeq -20$ MeVfm$^2$ at normal nuclear matter density
$\rho_0 = 0.16 $fm$^{-3}$. The strong $\Sigma N\to \Lambda N$ conversion
process contributes at the same time an imaginary part of $W_{\Sigma
ls}(k_{f0}) \simeq -12$ MeVfm$^2$. When combined with estimates of the
short-range contribution the total $\Sigma$-nuclear spin-orbit coupling becomes
rather weak.
