  The in-medium properties of a baryon-baryon interaction for the strangeness
$S=-2$ sector derived within chiral effective field theory up to
next-to-leading order are investigated. The considered $\Xi N$ interaction is
in line with available empirical constraints on the $\Lambda\Lambda$ $S$-wave
scattering length and on $\Xi N$ elastic and inelastic cross sections. In
particular, there are no near-threshold bound states in the $\Xi N$ system. A
conventional $G$-matrix calculation for this interaction is performed and
reveals that the single-particle potential of the $\Xi$-hyperon in nuclear
matter is moderately attractive as suggested by recent experimental evidence
for the existence of $\Xi$-hypernuclei.
