Theory holds that the capacity of a population to evolve in response to a selective pressure is due to the enrichment of pre-existing adaptive variants. That is, successful alleles are not produced by selection itself. This line of thinking has recently been challenged by the observation that some types of selection can induce mutations that confer an adaptive advantage. Although the generality of such findings is controversial, a number of induced mutagenesis systems have now been characterized at the genetic level in bacteria. Much less is known about whether and how such processes might operate in eukaryotic cells. The highly conserved molecular chaperone Hsp90, which assists in the folding of many proteins that are critical for growth and development, has been proposed to broadly influence the capacity of mutations to produce new phenotypes. Because the activity of Hsp90 is stress-regulated, we investigated whether it might provide a means through which the environment could influence acquisition of adaptive phenotypes. Using the classic statistical assay known as the fluctuation test, we observed that a modest change in Hsp90 activity altered the mechanisms by which yeast cells acquire resistance to the commonly prescribed antifungal drug fluconazole. The distribution of resistant variants we obtained suggested that fluconazole exposure itself likely induced the acquisition of resistant phenotypes. This process strongly depended upon Hsp90 activity; induced resistance was not observed in cells with reduced Hsp90 activity. Furthermore, pre-exposure to fluconazole increased the frequency at which cells acquired resistance to the unrelated selective agent 5-fluoroorotic acid, supporting the idea that fluconazole can induce genetic diversification. We observed similar results with the evolutionarily distant human pathogen Candida albicans. Our findings establish a means through which environmental stress might influence the fundamental mechanisms of adaptation in eukaryotes and further point to an unappreciated benefit of modulating Hsp90 activity as a strategy to overcome drug resistance in fungi.