In supersaturated isotropic mixtures of hard rods, smectic filaments have recently been observed. We propose a model for formation and growth of these filaments similar to the Hoffman-Lauritzen model for polymer crystallization. Filament thickness is determined by a compromise between maximizing the amount of smectic phase formed and minimizing the nucleation barrier for adding new segments to the growing filament. We compare our analytical results to kinetic Monte Carlo simulations