By analogy to other members of the Flaviviridae family, the hepatitis C virus (HCV) core protein is presumed to oligomerize to form the viral nucleocapsid, which encloses the single-stranded RNA genome. Core protein is directed to lipid droplets (LDs) by domain 2 (D2) of the protein, and this process is critical for virus production. Domain 1 (D1) of core is also important for infectious particle morphogenesis, although its precise contribution to this process is poorly understood. In this study, we mutated amino acids 64 to 75 within D1 of core and examined the ability of these mutants to produce infectious virus. We found that residues 64 to 66 are critical for generation of infectious progeny, whereas 67 to 75 were dispensable for this process. Further investigation of the defective 64 to 66 mutant (termed JFH1(T)-64-66) revealed it to be incapable of producing infectious intracellular virions, suggesting a fault during HCV assembly. Furthermore, isopycnic gradient analyses revealed that JFH1(T)-64-66 assembled dense intracellular species of core, presumably representing nucleocapsids. Thus, amino acids 64 to 66 are seemingly not involved in core oligomerization/nucleocapsid assembly. Passaging of JFH1(T)-64-66 led to the emergence of a single compensatory mutation (K1302R) within the helicase domain of NS3 that completely rescued its ability to produce infectious virus. Importantly, the same NS3 mutation abrogated virus production in the context of wild-type core protein. Together, our results suggest that residues 64 to 66 of core D1 form a highly specific interaction with the NS3 helicase that is essential for the generation of infectious HCV particles at a stage downstream of nucleocapsid assembly.