The self-diffusion coefficients D for neat CO2 have been determined in a wide rho, T range by the Stejskal-Tanner NMR method applying pulsed field gradients. In our apparatus CO2 supercools readily and the data could be collected between 223 K and 450 K at pressures up to 200 MPa. The rho, T dependence of D(CO2) shows significant deviation from hard-sphere fluid behavior. The rough hard sphere (RHS) model, as well as the simple hydrodynamic theory show a very unusual temperature dependence, when compared to other simple fluids.