The effect of oil on the equilibrium microstructure of a dilute micellar solution is investigated using lattice Monte Carlo techniques. Dramatic growth of the self-assembled micelles into elongated worms is observed as oil is solubilized within the oily tail region of the micelles. These results confirm a microscopic explanation for experimentally observed changes in the phase behavior of surfactant solutions as oil is added. In these simulations, a two-box simulation technique is used to guarantee that the micellar system is stable with respect to emulsification failure (the appearance of a bulk oil phase).