Cyclins are central engines of cell cycle progression in conjunction with cyclin-dependent kinases (CDKs). Among the different cyclins controlling cell cycle progression, cyclin F does not partner with a CDK, but instead forms via its F-box domain an SCF (Skp1-Cul1-F-box)-type E3 ubiquitin ligase module. Although various substrates of cyclin F have been identified, the vulnerabilities of cells lacking cyclin F are not known. Thus, we assessed viability of cells lacking cyclin F upon challenging them with more than 180 different kinase inhibitors. The screen revealed a striking synthetic lethality between Chk1 inhibition and cyclin F loss. Chk1 inhibition in cells lacking cyclin F leads to DNA replication catastrophe. Replication catastrophe depends on accumulation of the transcription factor E2F1 in cyclin F-depleted cells. We find that SCF-cyclin F controls E2F1 ubiquitylation and degradation during the G2/M phase of the cell cycle and upon challenging cells with Chk1 inhibitors. Thus, Cyclin F restricts E2F1 activity during the cell cycle and upon checkpoint inhibition to prevent DNA replication stress. Our findings pave the way for patient selection in the clinical use of checkpoint inhibitors.