Dysregulated expression of MYC family genes is a hallmark of many malignancies. Unfortunately, these proteins are not amenable to blockade by small molecules or protein-based therapeutic agents. Therefore, we must find alternative approaches to target MYC-driven cancers. Amplification of MYCN, a MYC family member, predicts high-risk neuroblastoma (NB) disease. We have shown that R9-caPep blocks the interaction of PCNA with its binding partners and selectively kills human NB cells, especially those with MYCN amplification, and we now show the mechanism. We found elevated levels of DNA replication stress in MYCN-amplified NB cells. R9-caPep exacerbated DNA replication stress in MYCN-amplified NB cells and NB cells with an augmented level of MYC by interfering with DNA replication fork extension, leading to Chk1 dependence and susceptibility to Chk1 inhibition. We describe how these effects may be exploited for treating NB.