Hepatitis C virus (HCV) NS5A is essential for viral genome replication within cytoplasmic replication complexes and virus assembly at the lipid droplet (LD) surface, although its definitive functions are poorly understood. We developed approaches to investigate NS5A dynamics during a productive infection. We report here that NS5A motility and efficient HCV RNA replication require the microtubule network and the cytoplasmic motor dynein and demonstrate that both motile and relatively static NS5A-positive foci are enriched with host factors VAP-A and Rab5A. Pulse-chase imaging revealed that newly synthesized NS5A foci are small and distinct from aged foci, while further studies using a unique dual fluorescently tagged infectious HCV chimera showed a relatively stable association of NS5A foci with core-capped LDs. These results reveal new details about the dynamics and maturation of NS5A and the nature of potential sites of convergence of HCV replication and assembly pathways.