Breaks at common fragile sites (CFS) are a recognized source of genome instability in pre-neoplastic lesions, but how such checkpoint-proficient cells escape surveillance and continue cycling is unknown. Here we show, in lymphocytes and fibroblasts, that moderate replication stresses like those inducing breaks at CFSs trigger chromatin loading of sensors and mediators of the ATR pathway but fail to activate Chk1 or p53. Consistently, we found that cells depleted of ATR, but not of Chk1, accumulate single-stranded DNA upon Mre11-dependent resection of collapsed forks. Partial activation of the pathway under moderate stress thus takes steps against fork disassembly but tolerates S-phase progression and mitotic onset. We show that fork protection by ATR is crucial to CFS integrity, specifically in the cell type where a given site displays paucity in backup replication origins. Tolerance to mitotic entry with under-replicated CFSs therefore results in chromosome breaks, providing a pool of cells committed to further instability.