Abstract : Results on the production of the double-strange cascade hyperon Ξ− are reported for collisions of p\,(3.5~GeV)\,+\,Nb, studied with the High Acceptance Di-Electron Spectrometer (HADES) at SIS18 at GSI Helmholtzzentrum for Heavy-Ion Research, Darmstadt. For the first time, subthreshold Ξ− production is observed in proton-nucleus interactions. Assuming a Ξ− phase-space distribution similar to that of Λ hyperons, the production probability amounts to PΞ−=(2.0±0.4(stat)±0.3(norm)±0.6(syst))×10−4 resulting in a Ξ−/(Λ+Σ0) ratio of PΞ−/ PΛ+Σ0=(1.2±0.3(stat)±0.4(syst))×10−2. Available model predictions are significantly lower than the estimated Ξ− yield.