The dynamics of phase separation in a symmetric three-component two-dimensional fluid system is investigated by a molecular-dynamics approach. In contrast to concentrated binary fluids, we find that the ternary system at late times reaches a dynamical scaling regime during which the domains grow as t^1/3, in agreement with the classical theory of Lifshitz and Slyozov. This finding, which we relate to the compact structure of the separating domains, implies that hydrodynamic flow is likely not to control the separation process in a ternary-fluid system.