Local adaptation directs populations towards environment-specific fitness maxima through acquisition of positively selected traits. However, rapid environmental changes can identify hidden fitness trade-offs that turn adaptation into maladaptation, resulting in evolutionary traps. Cancer, a disease that is prone to drug resistance, is in principle susceptible to such traps. We therefore performed pooled CRISPR–Cas9 knockout screens in acute myeloid leukemia (AML) cells treated with various chemotherapies to map the drug-dependent genetic basis of fitness trade-offs, a concept known as antagonistic pleiotropy (AP). We identified a PRC2–NSD2/3-mediated MYC regulatory axis as a drug-induced AP pathway whose ability to confer resistance to bromodomain inhibition and sensitivity to BCL-2 inhibition templates an evolutionary trap. Across diverse AML cell-line and patient-derived xenograft models, we find that acquisition of resistance to bromodomain inhibition through this pathway exposes coincident hypersensitivity to BCL-2 inhibition. Thus, drug-induced AP can be leveraged to design evolutionary traps that selectively target drug resistance in cancer.