A continuous-flow process based on a chiral transition-metal complex in a supported ionic liquid phase (SILP) with supercritical carbon dioxide (scCO2) as the mobile phase is presented for asymmetric catalytic transformations of low-volatility organic substrates at mild reaction temperatures. Enantioselectivity of >99 % ee and quantitative conversion were achieved in the hydrogenation of dimethylitaconate for up to 30 h, reaching turnover numbers beyond 100 000 for the chiral QUINAPHOS–rhodium complex. By using an automated high-pressure continuous-flow setup, the product was isolated in analytically pure form without the use of any organic co-solvent and with no detectable catalyst leaching. Phase-behaviour studies and high-pressure NMR spectroscopy assisted the localisation of optimum process parameters by quantification of substrate partitioning between the IL and scCO2. Fundamental insight into the molecular interactions of the metal complex, ionic liquid and the surface of the support in working SILP catalyst materials was gained by means of systematic variations, spectroscopic studies and labelling experiments. In concert, the obtained results provided a rationale for avoiding progressive long-term deactivation. The optimised system reached stable selectivities and productivities that correspond to 0.7 kg L−1 h−1 space–time yield and at least 100 kg product per gram of rhodium, thus making such processes attractive for larger-scale application.