  Brueckner theory is used to investigate the in-medium properties of a
$\Lambda$-hyperon in nuclear and neutron matter, based on hyperon-nucleon
interactions derived within SU(3) chiral effective field theory (EFT). It is
shown that the resulting $\Lambda$ single-particle potential
$U_\Lambda(p_\Lambda =0,\rho)$ becomes strongly repulsive for densities $\rho$
of two-to-three times that of normal nuclear matter. Adding a density-dependent
effective $\Lambda N$-interaction constructed from chiral $\Lambda NN$
three-body forces increases the repulsion further. Consequences of these
findings for neutron stars are discussed. It is argued that for hyperon-nuclear
interactions with properties such as those deduced from the SU(3) EFT
potentials, the onset for hyperon formation in the core of neutron stars is
expected to be shifted to extremely high baryon density, thus potentially
resolving the so-called hyperon puzzle.
