The main focus of this paper is to present experimental and simulation results that describe CO2 injection in a chalk sample with fracture-matrix interaction at reservoir conditions. Based on the experiments, simulation models are built to mimic the main transport phenomena, including diffusion, which is found to be particularly important. The first two experiments consist of a vertically-oriented 7.4 cm long Sigerslev outcrop chalk core with a 3.7 cm diameter. A single "fracture" is represented by a centralized hole with a 0.6 cm diameter along the core, giving a pore-to-fracture volume ratio of 18. Both matrix and fracture are initially saturated with a North Sea stock tank oil (STO) at 110°C and 258 bara. Once the initial conditions are established, CO2 is injected from the top of the fracture and the oil is produced from the bottom. Injected CO2 diffuses into the oil in the matrix and swells the oil. Once the oil in the fracture has drained, the matrix feeds the fracture with oil at decreasing rates, with the test lasting up to 440 hours (∼34 pore-volume-injected, PVinj). The third experiment is similar, but laboratory oil n-C10 (Lab-Oil) is used instead of STO. Lab-Oil and CO2 have very similar densities at the chosen experimental conditions, which minimizes gravity-driven convective (Darcy) transport and maximizes the impact of diffusion. Our modeling is conducted with a compositional reservoir simulator. A tuned equation of state (EOS) model accounts for proper estimation of the phase and volumetric properties for CO2 mixtures in the STO and n-C10 systems. Automated history matching is used to fit the experimental data. Numerical simulations are conducted to match experimental oil production data by tuning the oil and gas diffusion coefficients. Good agreement between the numerical model and the experimental data is obtained. For the n-C10 system in particular, we find the results are not sensitive to vertical permeability, confirming displacement is dominated by diffusion rather than convective flux. Verifying the accuracy of modeling the diffusion-dominated processes in a fractured chalk system with CO2 at reservoir conditions has been accomplished. This is an important step towards modeling an actual fractured chalk / reservoir oil system undergoing CO2 injection. The experimental and modeling results demonstrate a method to isolate diffusion-driven transport in a fracture-matrix chalk system at reservoir conditions. A commercial reservoir simulator is able to reproduce laboratory results adequately.