Hepatitis C virus (HCV) infects liver cells and often causes chronic infection, also leading to liver cirrhosis and cancer. In the cytoplasm, the viral structural and non-structural (NS) proteins are directly translated from the plus strand HCV RNA genome. The viral proteins NS3 to NS5B proteins constitute the replication complex that is required for RNA genome replication via a minus strand antigenome. The most C-terminal protein in the genome is the NS5B replicase, which needs to initiate antigenome RNA synthesis at the very 3′-end of the plus strand. Using ribosome profiling of cells replicating full-length infectious HCV genomes, we uncovered that ribosomes accumulate at the HCV stop codon and about 30 nucleotides upstream of it. This pausing is due to the presence of conserved rare, inefficient Wobble codons upstream of the termination site. Synonymous substitution of these inefficient codons to efficient codons has negative consequences for viral RNA replication but not for viral protein synthesis. This pausing may allow the enzymatically active replicase core to find its genuine RNA template in cis, while the protein is still held in place by being stuck with its C-terminus in the exit tunnel of the paused ribosome.