Chronic hepatitis C virus (HCV) infection is one of the leading causes of liver failure and liver cancer, affecting around 3% of the world's population. The extreme sequence variability of the virus resulting from error-prone replication has thwarted the discovery of a universal prophylactic vaccine. It is known that vigorous and multispecific cellular immune responses, involving both helper CD4+ and cytotoxic CD8+ T cells, are associated with the spontaneous clearance of acute HCV infection. Escape mutations in viral epitopes can, however, abrogate protective T-cell responses, leading to viral persistence and associated pathologies. Despite the propensity of the virus to mutate, there might still exist substitutions that incur a fitness cost. In this paper, we identify groups of coevolving residues within HCV nonstructural protein 3 (NS3) by analyzing diverse sequences of this protein using ideas from random matrix theory and associated methods. Our analyses indicate that one of these groups comprises a large percentage of residues for which HCV appears to resist multiple simultaneous substitutions. Targeting multiple residues in this group through vaccine-induced immune responses should either lead to viral recognition or elicit escape substitutions that compromise viral fitness. Our predictions are supported by published clinical data, which suggested that immune genotypes associated with spontaneous clearance of HCV preferentially recognized and targeted this vulnerable group of residues. Moreover, mapping the sites of this group onto the available protein structure provided insight into its functional significance. An epitope-based immunogen is proposed as an alternative to the NS3 epitopes in the peptide-based vaccine IC41.