Antiviral treatment of HIV-1 infection often fails because of the rapid emergence of resistant virus within weeks of the start of therapy. This raises the question of whether resistant viruses pre-exist in drug-naive patients or whether it is produced after the start of therapy. Here we compare the likelihood of pre-existence with the likelihood of production of resistant virus during therapy. We show that provided resistant virus pre-exists, then a stronger therapy may lead to a greater initial reduction of virus load, but will also cause a faster rise of resistant virus. In this case the total benefit of treatment is independent of the degree of inhibition of sensitive virus. If, on the other hand, resistant mutants do not pre-exist, then the emergence of resistance during treatment depends on the efficacy of the drug. If the drug is sufficiently potent to eradicate sensitive virus, then the probability that resistant mutants first appear during therapy is smaller than the probability that they existed before therapy. If the drug cannot eradicate the sensitive virus, then after sufficiently long time resistant mutants will appear. However, mutants that are unlikely to pre-exist may taken long time to appear.