  The first experimental information on the strong interaction between
$\Lambda$ and $\Xi^-$ strange baryons is presented in this Letter. The
correlation function of $\Lambda-\Xi^-$ and
$\overline{\Lambda}-\overline{\Xi}^{+}$ pairs produced in high-multiplicity
proton-proton (pp) collisions at $\sqrt{s}$ = 13 TeV at the LHC is measured as
a function of the relative momentum of the pair. The femtoscopy method is used
to calculate the correlation function, which is then compared with theoretical
expectations obtained using a meson exchange model, chiral effective field
theory, and Lattice QCD calculations close to the physical point. Data support
predictions of small scattering parameters while discarding versions with large
ones, thus suggesting a weak $\Lambda-\Xi^{-}$ interaction. The limited
statistical significance of the data does not yet allow one to constrain the
effects of coupled channels like $\Sigma-\Xi$ and N$-\Omega$.
