Cytotoxic T lymphocytes (CTLs) are key to the antiviral immune response. For a given virus, a typical host has several kinds of CTLs that are each specific for a different epitope of the virus. RNA viruses often exhibit high rates of mutation, and mutation in the viral epitopes is an important mechanism by which these viruses may escape the CTLs. We would like to know the probability that a wild-type virus will accumulate mutations in all recognizable epitopes before being eliminated by CTLs. We present a stochastic model that enables efficient calculation of this probability. Our results are compared with the behaviour of an analogous deterministic model.