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.