The emergence of X4 tropic viral strains throughout the course of HIV infection is associated with poorer prognostic outcomes and faster progressions to AIDS than for patients in whom R5 viral strains predominate. Here we investigate a stochastic model to account for the emergence of X4 virus via mutational intermediates of lower fitness that exhibit dual/mixed (D/M) tropism, and employ the model to investigate whether the administration of CCR5 blockers in-vivo is likely to promote a shift towards X4 tropism. We show that the proposed stochastic model can account for X4 emergence with a median time of approximately 4 years post-infection as a result of: 1.) random stochastic mutations in the V3 region of env during the reverse transcription step of infection; 2.) increasing numbers of CXCR4-expressing activated naive CD4+ T cells with declining total CD4+ T cell counts, thereby providing increased numbers of activated target cells for productive infection by X4 virus. Our model indicates that administration of the CCR5 blocker maraviroc does not promote a shift towards X4 tropism, assuming sufficient efficacy of background therapy (BT). However our modelling also indicates that administration of maraviroc as a monotherapy or with BT of suboptimal efficacy can promote emergence of X4 tropic virus, resulting in accelerated progression to AIDS. Taken together, our results demonstrate that maraviroc is safe and effective if co-administered with sufficiently potent BT, but that suboptimal BT may promote X4 emergence and accelerated progression to AIDS. These results underscore the clinical importance for careful selection of BT when CCR5 blockers are administered in-vivo.