The evolution of drug resistance in microbial pathogens provides a paradigm for investigating evolutionary dynamics with important consequences for human health. Candida albicans, the leading fungal pathogen of humans, rapidly evolves resistance to two major antifungal classes, the triazoles and echinocandins. In contrast, resistance to the third major antifungal used in the clinic, amphotericin B (AmB), remains extremely rare despite 50 years of use as monotherapy. We sought to understand this long-standing evolutionary puzzle. We used whole genome sequencing of rare AmB-resistant clinical isolates as well as laboratory-evolved strains to identify and investigate mutations that confer AmB resistance in vitro. Resistance to AmB came at a great cost. Mutations that conferred resistance simultaneously created diverse stresses that required high levels of the molecular chaperone Hsp90 for survival, even in the absence of AmB. This requirement stemmed from severe internal stresses caused by the mutations, which drastically diminished tolerance to external stresses from the host. AmB-resistant mutants were hypersensitive to oxidative stress, febrile temperatures, and killing by neutrophils and also had defects in filamentation and tissue invasion. These strains were avirulent in a mouse infection model. Thus, the costs of evolving resistance to AmB limit the emergence of this phenotype in the clinic. Our work provides a vivid example of the ways in which conflicting selective pressures shape evolutionary trajectories and illustrates another mechanism by which the Hsp90 buffer potentiates the emergence of new phenotypes. Developing antibiotics that deliberately create such evolutionary constraints might offer a strategy for limiting the rapid emergence of drug resistance.