Inactivation of SMARCA4/BRG1, the core ATPase subunit of mammalian SWI/SNF complexes, occurs at very high frequencies in non-small cell lung cancers (NSCLC). There are no targeted therapies for this subset of lung cancers, nor is it known how mutations in BRG1 contribute to lung cancer progression. Using a combination of gain- and loss-of-function approaches, we demonstrate that deletion of BRG1 in lung cancer leads to activation of replication stress responses. Single-molecule assessment of replication fork dynamics in BRG1-deficient cells revealed increased origin firing mediated by the prelicensing protein, CDC6. Quantitative mass spectrometry and coimmunoprecipitation assays showed that BRG1-containing SWI/SNF complexes interact with RPA complexes. Finally, BRG1-deficient lung cancers were sensitive to pharmacologic inhibition of ATR. These findings provide novel mechanistic insight into BRG1-mutant lung cancers and suggest that their dependency on ATR can be leveraged therapeutically and potentially expanded to BRG1-mutant cancers in other tissues.