  We present a novel approach to the density dependent mean field and the
spin-orbit interaction of a $\Lambda$-hyperon in a nuclear many-body system,
based on flavor-SU(3) in-medium chiral perturbation theory. The leading
long-range $\Lambda N$-interaction arises from kaon exchange and from two-pion
exchange with a $\Sigma$-hyperon in the intermediate state. The empirical
$\Lambda$-nucleus potential depth of about $-28 $MeV is well reproduced with a
single cutoff scale, $\bar \Lambda = 0.7 $GeV, effectively representing all
short-distance (high-momentum) dynamics not resolved at scales characteristic
of the nuclear Fermi momentum. This value of $\bar\Lambda$ is remarkably
consistent with the one required to reproduce the empirical saturation point of
isospin-symmetric nuclear matter in the same framework. The smallness of the
$\Lambda$-nuclear spin-orbit interaction finds a natural (yet novel)
explanation in terms of an almost complete cancellation between short-range
contributions (properly rescaled from the known nucleonic spin-orbit coupling
strength) and long-range terms generated by iterated one-pion exchange with
intermediate $\Sigma$-hyperons. The small $\Sigma\Lambda$-mass difference
figures prominently in this context.
