We report first results on a deep sub-threshold production of the doubly strange hyperon $Xi^-$ in a heavy-ion reaction. At a beam energy of 1.76A GeV the reaction Ar+KCl was studied with the High Acceptance Di-Electron Spectrometer (HADES) at SIS18/GSI. A high-statistics and high-purity $Lambda$ sample was collected, allowing for the investigation of the decay channel $Xi^- to Lambda pi^-$. The deduced $Xi^-/(Lambda+Sigma^0)$ production ratio of $(5.6 pm 1.2 ^{+1.8}_{-1.7})cdot 10^{-3}$ is significantly larger than available model predictions.