Sex allows beneficial mutations that occur in separate lineages to be fixed in the same genome. For this reason, the Fisher-Muller model predicts that adaptation to the environment is more rapid in a large sexual population than in an equally large asexual population. Sexual reproduction occurs in populations of the RNA virus Φ6 when multiple bacteriophages coinfect the same host cell. Here, we tested the model’s predictions by determining whether sex favors more rapid adaptation of Φ6 to a bacterial host, Pseudomonas phaseolicola. Replicate populations of Φ6 were allowed to evolve in either the presence or absence of sex for 250 generations. All experimental populations showed a significant increase in fitness relative to the ancestor, but sex did not increase the rate of adaptation. Rather, we found that the sexual and asexual treatments also differ because intense intrahost competition between viruses occurs during coinfection. Results showed that the derived sexual viruses were selectively favored only when coinfection is common, indicating that within-host competition detracts from the ability of viruses to exploit the host. Thus, sex was not advantageous because the cost created by intrahost competition was too strong. Our findings indicate that high levels of coinfection exceed an optimum where sex may be beneficial to populations of Φ6, and suggest that genetic conflicts can evolve in RNA viruses.