  We have solved for the first time the Faddeev equations for the bound state
problem of the coupled $\Lambda\Lambda N$--$\Xi NN$ system to study whether an
hypertriton with strangeness -2 may exist or not. We make use of the
interactions obtained from a chiral quark model describing the low-energy
observables of the two-baryon systems with strangeness 0, -1, and -2 and
three-baryon systems with strangeness 0 and -1. The $\Lambda\Lambda N$ system
alone is unbound. However, when the full coupling to $\Xi NN$ is considered,
the strangeness -2 three-baryon system with quantum numbers
$(I,J^P)=(1/2,1/2^+)$ becomes bound, with a binding energy of about 0.5 MeV.
This result is compatible with the non-existence of a stable $^3_\Lambda$H with
isospin one.
