The rapid evolution of drug resistance remains a major obstacle for HIV therapy. The capacity of the virus for recombination is widely believed to facilitate the evolution of drug resistance. Here, we challenge this intuitive view. We develop a population genetic model of HIV replication that incorporates the processes of mutation, cellular superinfection, and recombination. We show that cellular superinfection increases the abundance of low fitness viruses at the expense of the fittest strains due to the mixing of viral proteins during virion assembly. Moreover, we argue that whether recombination facilitates the evolution of drug resistance depends critically on how resistance mutations interact to determine viral fitness. Contrary to the commonly held belief, we find that, under the most plausible biological assumptions, recombination is expected to slow down the rate of evolution of multi-drug-resistant virus during therapy.