Infection by hepatitis C virus (HCV) leads to one of two outcomes; either the infection resolves within approximately 6 months or the virus can persist indefinitely. Host genetics are known to affect the likelihood of clearance or persistence. By contrast, the importance of the virus genotype in determining infection outcome is unknown, as quantifying this effect traditionally requires well-characterized transmission networks, which are rare. Extending phylogenetic approaches previously developed to estimate the virus control over set-point viral load in HIV-1 infections, we simulate inheritance of a binary trait along a phylogenetic tree, use this data to quantify how infection outcomes cluster and ascertain the effect of virus genotype on these. We apply our method to the Hepatitis C Incidence and Transmission Study in prisons (HITS-p) data set from Australia, as this cohort prospectively identified incident cases including viraemic subjects who ultimately clear the virus, thus providing us with a unique collection of sequences from clearing infections. We detect significant correlations between infection outcome and virus distance in the phylogeny for viruses of Genotype 1, with estimates lying at around 67%. No statistically significant estimates were obtained for viruses of Genotype 3a.