The development of cancer therapies may be improved by the discovery of tumor-specific molecular dependencies. The requisite tools include genetic and chemical perturbations, each with its strengths and limitations. Chemical perturbations can be readily applied to primary cancer samples at large scale, but mechanistic understanding of hits and further pharmaceutical development is often complicated by the fact that a chemical compound has affinities to multiple proteins. To computationally infer specific molecular dependencies of individual cancers from their ex vivo drug sensitivity profiles, we developed a mathematical model that deconvolutes these data using measurements of protein-drug affinity profiles. Through integrating a drug-kinase profiling dataset and several drug response datasets, our method, DepInfeR, correctly identified known protein kinase dependencies, including the EGFR dependence of HER2+ breast cancer cell lines, the FLT3 dependence of acute myeloid leukemia (AML) with FLT3-ITD mutations and the differential dependencies on the B-cell receptor pathway in the two major subtypes of chronic lymphocytic leukemia (CLL). Furthermore, our method uncovered new subgroup-specific dependencies, including a previously unreported dependence of high-risk CLL on Checkpoint kinase 1 (CHEK1). The method also produced a detailed map of the kinase dependencies in a heterogeneous set of 117 CLL samples. The ability to deconvolute polypharmacological phenotypes into underlying causal molecular dependencies should increase the utility of high-throughput drug response assays for functional precision oncology.