Strains of the influenza virus form coherent global populations, yet exist at the level of single infections in individual hosts. The relationship between these scales is a critical topic for understanding viral evolution. Here we investigate the within-host relationship between selection and the stochastic effects of genetic drift, estimating an effective population size of infection Ne for influenza infection. Examining whole-genome sequence data describing a chronic case of influenza B in a severely immunocompromised child we infer an Ne of 2.5 × 107 (95% confidence range 1.0 × 107 to 9.0 × 107) suggesting that genetic drift is of minimal importance during an established influenza infection. Our result, supported by data from influenza A infection, suggests that positive selection during within-host infection is primarily limited by the typically short period of infection. Atypically long infections may have a disproportionate influence upon global patterns of viral evolution.