Abstract: Results on the deep sub-threshold production of the short-lived hadronic resonance K*(892)(0) are reported for collisions of Ar + KCl at 1.76 A GeV beam energy, studied with the High Acceptance Di-Electron Spectrometer (HADES) at SIS18/GSI. The K*(892)(0) production probability per central collision of P-K*0 = (4.4 +/- 1.1 +/- 0.5) x 10(-4) and the K*(892)(0)/K-0 ratio of P-K*0/P-K0 = (1.9 +/- 0.5 +/- 0.3) x 10(-2) are determined at the lowest energy so far (i.e. deep below the threshold for the corresponding production in nucleon-nucleon collisions, root s(NN)-root s(thr) = -340MeV). The K*(0)/K-0 ratio is compared with results of other experiments and with the predictions of the UrQMD transport approach and of the statistical hadronization model. The experimental K*(0) yield and the K-*0/K-0 ratio are overestimated by the transport model by factors of about five and two, respectively. In a chemically equilibrated medium the ratio corresponds to a temperature of the thermalized system being systematically lower than the value determined by the yields of the stable and long-lived hadrons produced in Ar + KCl collisions. From the present measurement, we conclude that sub-threshold K* production either cannot be considered to proceed in a system being in thermal equilibrium or these short-lived resonances appear undersaturated, for example as a result of the rescattering of the decay particles in the ambient hadronic medium.