  Using chiral perturbation theory, we calculate the density-dependent
spin-orbit coupling generated by the two-pion exchange three-nucleon
interaction involving virtual $\Delta$-isobar excitation. From the
corresponding three-loop Hartree and Fock diagrams we obtain an isoscalar
spin-orbit strength $F_{\rm so}(k_f)$ which amounts at nuclear matter
saturation density to about half of the empirical value of $90 $MeVfm$^5$. The
associated isovector spin-orbit strength $G_{\rm so}(k_f)$ comes out about a
factor of 20 smaller. Interestingly, this three-body spin-orbit coupling is not
a relativistic effect but independent of the nucleon mass $M$. Furthermore, we
calculate the three-body spin-orbit coupling generated by two-pion exchange on
the basis of the most general chiral $\pi\pi NN$-contact interaction. We find
similar (numerical) results for the isoscalar and isovector spin-orbit
strengths $F_{\rm so}(k_f)$ and $G_{\rm so}(k_f)$ with a strong dominance of
the p-wave part of the $\pi\pi NN$-contact interaction and the Hartree
contribution.
