Bacteriophages are the most abundant and genetically diverse life forms, even greater than their numerous bacterial prey. This observation seems to violate fundamental ecological theory that predicts higher trophic levels should be less diverse than lower trophic levels, leading to the question of what mechanisms could support greater parasite diversity than host diversity. Here we provide unexpected results from a bacteriophage λ evolution experiment where λ was continually supplied a single isogenic host, yet repeatedly evolved a diversity of genotypes that diverged in their receptor use. Measurements of negative frequency-dependent selection between the receptor specialists revealed that they evolved because of diversifying selection. Such selection in viruses usually stems from adaptations to specialize on different hosts, but only a single host was provided and replenished every eight hours. A series of experiments conducted over the 8-hour incubation period revealed that selection for the different specialist phages oscillated because gene expression of the two receptors oscillated (E. coli outer membrane proteins LamB and OmpF). The cause of the receptor expression changes was in part attributable to rapid evolution in the bacteria within the eight-hour period that was documented through both phenotypic resistance assays and population genome sequencing. Altogether this suggests that rapid host evolution on the timescales of hours can drive the emergence of multiple host genotypes and their oscillations can promote the evolution of phage diversity. This result suggests that rapid host evolution may play a role in driving viral diversity and may promote diversity in other non-microbial systems too.