In this contribution, we report on an investigation of the possible existence of bound $\Xi$ states in systems with $A=4-7$ baryons using the Jacobi NCSM approach in combination with chiral NN and $\Xi$N interactions. Three shallow bound states for the NNN$\Xi$ system (with $(J^\pi,T)=(1^+,0)$, $(0^+,1)$ and $(1^+,1)$) with quite similar binding energies are found. The $^5_{\Xi}\mathrm{H}(\frac{1}{2}^+,\frac{1}{2})$ and $^7_{\Xi}\mathrm{H}(\frac{1}{2}^+,\frac{3}{2})$ hypernuclei are also clearly bound with respect to the thresholds $^4\mathrm{He} + \Xi$ and $^6\mathrm{He} +\Xi$, respectively. It is also found that the binding of these systems is predominantly due the attraction of the chiral $\Xi$N potential particularly in the $^{33}S_{1}$ channel. Furthermore, a perturbative estimate suggests that the decay widths of all the bound states could be small enough for them to be observed in experiment.