Long-term storage of high-level nuclear waste glass in France is expected to occur in an engineered barrier system (EBS) located in a subsurface Callovo-Oxfordian (COx) clay rock formation in the Paris Basin in northeastern France. Understanding the behavior of glass dissolution in the complex system is critical to be able to reliably model the performance of the glass in this complex environment. To simulate this multi-barrier repository scenario in the laboratory, several tests have been performed to measure glass dissolution rates of the simulated high-level nuclear waste glass, SON68, in the presence of COx claystone at 90 °C. Experiments utilized a High-Performance Liquid Chromatography (HPLC) pump to pass simulated Bure site COx pore water through a reaction cell containing SON68 placed between two COx claystone cores for durations up to 200 days. Silicon concentrations at the outlet were similar in all experiments, even the blank experiment with only the COx claystone (∼4 mg/L at 25 °C and ∼15 mg/L at 90 °C). The steady-state pH of the effluent, measured at room temperature, was roughly 7.1 for the blank and 7.3–7.6 for the glass-containing experiments demonstrating the pH buffering capacity of the COx claystone. Dissolution rates for SON68 in the presence of the claystone were elevated compared to those obtained from flow-through experiments conducted with SON68 without claystone in silica-saturated solutions at the same temperature and similar pH values. Additionally, through surface examination of the monoliths, the side of the monolith in direct contact with the claystone was seen to have a corrosion thickness 2.5× greater than the side in contact with the bulk glass powder. Results from one experiment containing 32Si-doped SON68 also suggest that the movement of Si through the claystone is controlled by a chemically coupled transport with a Si retention factor, Kd, of 900 mL/g.