Oncogene-induced DNA replication stress contributes critically to the genomic instability that is present in cancer. However, elucidating how oncogenes deregulate DNA replication has been impeded by difficulty in mapping replication initiation sites on the human genome. Here, using a sensitive assay to monitor nascent DNA synthesis in early S phase, we identified thousands of replication initiation sites in cells before and after induction of the oncogenes CCNE1 and MYC. Remarkably, both oncogenes induced firing of a novel set of DNA replication origins that mapped within highly transcribed genes. These ectopic origins were normally suppressed by transcription during G1, but precocious entry into S phase, before all genic regions had been transcribed, allowed firing of origins within genes in cells with activated oncogenes. Forks from oncogene-induced origins were prone to collapse, as a result of conflicts between replication and transcription, and were associated with DNA double-stranded break formation and chromosomal rearrangement breakpoints both in our experimental system and in a large cohort of human cancers. Thus, firing of intragenic origins caused by premature S phase entry represents a mechanism of oncogene-induced DNA replication stress that is relevant for genomic instability in human cancer.