Copy number heterogeneity is a prominent feature within tumors. The molecular basis for this heterogeneity remains poorly characterized. Here, we demonstrate that hypoxia induces transient site-specific copy gains (TSSGs) in primary, nontransformed, and transformed human cells. Hypoxia-driven copy gains are not dependent on HIF1α or HIF2α; however, they are dependent on the KDM4A histone demethylase and are blocked by inhibition of KDM4A with a small molecule or the natural metabolite succinate. Furthermore, this response is conserved at a syntenic region in zebrafish cells. Regions with site-specific copy gain are also enriched for amplifications in hypoxic primary tumors. These tumors exhibited amplification and overexpression of the drug resistance gene CKS1B, which we recapitulated in hypoxic breast cancer cells. Our results demonstrate that hypoxia provides a biological stimulus to create transient site-specific copy alterations that could result in heterogeneity within tumors and cell populations. These findings have major implications in our understanding of copy number heterogeneity and the emergence of drug resistance genes in cancer.