Because cytotoxic T-lymphocytes (CTLs) have been shown to play a role in controlling human immunodeficiency virus (HIV) infection and because CTL-based simian immunodeficiency virus (SIV) vaccines have proved effective in non-human primates, one goal of HIV vaccine design is to elicit effective CTL responses in humans. Such a vaccine could improve viral control in patients who later become infected, thereby reducing onwards transmission and enhancing life expectancy in the absence of treatment. The ability of HIV to evolve mutations that evade CTLs and the ability of these escape mutants to spread amongst the population poses a challenge to the development of an effective and robust vaccine. We present a mathematical model of within-host evolution and between-host transmission of CTL escape mutants amongst a population receiving a vaccine that elicits CTL responses to multiple epitopes. Within-host evolution at each epitope is represented by the outgrowth of escape mutants in hosts who restrict the epitope and their reversion in hosts who do not restrict the epitope. We use this model to investigate how the evolution and spread of escape mutants could affect the impact of a vaccine. We show that in the absence of escape, such a vaccine could markedly reduce the prevalence of both infection and disease in the population. However the impact of such a vaccine could be significantly abated by CTL escape mutants, especially if their selection in hosts who restrict the epitope is rapid and their reversion in hosts who do not restrict the epitope is slow. We also use the model to address whether a vaccine should span a broad or narrow range of CTL epitopes and target epitopes restricted by rare or common HLA types. We discuss the implications and limitations of our findings.