An approach for computing Fick diffusivities directly from equilibrium molecular dynamics (MD) simulations is presented and demonstrated for a ternary chloroform-acetone-methanol liquid mixture. In our approach, Fick diffusivities are calculated from the Maxwell-Stefan (MS) diffusivities and the so-called matrix of thermodynamic factors. MS diffusivities describe the friction between different molecular species and can be directly computed from MD simulations. The thermodynamic factor describes the deviation from ideal mixing behavior and is difficult to extract from both experiments and simulations. Here, we show that the thermodynamic factor in ternary systems can be obtained from density fluctuations in small subsystems embedded in a larger simulation box. Since the computation uses the Kirkwood-Buff coefficients, the present approach provides a general route toward the thermodynamics of the mixture. In experiments, Fick diffusion coefficients are measured, while previously equilibrium molecular dynamics simulation only provided MS transport diffusivities. Our approach provides an efficient and accurate route to predict multicomponent diffusion coefficients in liquids based on a consistent molecular picture and therefore bridges the gap between theory and experiment.