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. Author summary: As survival and proliferation of cancer cells depend on molecular aberrations that can be highly specific to cancer types and individual tumors, identifying such dependence is pivotal to designing individualized tumor therapy. Chemical perturbations, through screening of bioactive compounds using primary cancer cells, provide an important tool for identifying tumor-specific dependencies. However, many chemical compounds bind multiple proteins, which complicates interpreting screening results and pinpointing the phenotype-causing target. To overcome this challenge and increase the utility of drug screening approaches for functional precision medicine, we developed a computational framework, DepInfeR, to identify tumor-specific dependencies on druggable proteins through integrating two sources of information: drug sensitivity assays and drug-protein affinity profiling. Our approach correctly identifies known kinase dependencies, which validates our approach. Furthermore, by integrating a newly generated drug screening dataset on primary tumor samples, we discovered a previously unreported survival dependence on Checkpoint kinase 1 (CHEK1) by a molecular subgroup of chronic lymphocytic leukemia samples, highlighting the clinical potential of our method. [ABSTRACT FROM AUTHOR]