Checkpoint kinase 1 (CHK1; encoded by CHEK1) is an essential gene that monitors DNA replication fidelity and prevents mitotic entry in the presence of under‐replicated DNA or exogenous DNA damage. Cancer cells deficient in p53 tumor suppressor function reportedly develop a strong dependency on CHK1 for proper cell cycle progression and maintenance of genome integrity, sparking interest in developing kinase inhibitors. Pharmacological inhibition of CHK1 triggers B‐Cell CLL/Lymphoma 2 (BCL2)‐regulated cell death in malignant cells largely independently of p53, and has been suggested to kill p53‐deficient cancer cells even more effectively. Next to p53 status, our knowledge about factors predicting cancer cell responsiveness to CHK1 inhibitors is limited. Here, we conducted a genome‐wide CRISPR/Cas9‐based loss‐of‐function screen to identify genes defining sensitivity to chemical CHK1 inhibitors. Next to the proapoptotic BCL2 family member, BCL2 Binding Component 3 (BBC3; also known as PUMA), the F‐box protein S‐phase Kinase‐Associated Protein 2 (SKP2) was validated to tune the cellular response to CHK1 inhibition. SKP2 is best known for degradation of the Cyclin‐dependent Kinase Inhibitor 1B (CDKN1B; also known as p27), thereby promoting G1‐S transition and cell cycle progression in response to mitogens. Loss of SKP2 resulted in the predicted increase in p27 protein levels, coinciding with reduced DNA damage upon CHK1‐inhibitor treatment and reduced cell death in S‐phase. Conversely, overexpression of SKP2, which consequently results in reduced p27 protein levels, enhanced cell death susceptibility to CHK1 inhibition. We propose that assessing SKP2 and p27 expression levels in human malignancies will help to predict the responsiveness to CHK1‐inhibitor treatment.