Outcomes of hepatitis C virus (HCV) infection and treatment depend on viral and host genetic factors. We use human genome-wide genotyping arrays and new whole-genome HCV viral sequencing technologies to perform a systematic genome-to-genome study of 542 individuals chronically infected with HCV, predominately genotype 3. We show that both HLA alleles and interferon lambda innate immune system genes drive viral genome polymorphism, and that IFNL4 genotypes determine HCV viral load through a mechanism that is dependent on a specific polymorphism in the HCV polyprotein. We highlight the interplay between innate immune responses and the viral genome in HCV control.