Acquired chromosomal instability and copy number alterations are hallmarks of cancer. Enzymes capable of promoting site-specific copy number changes have yet to be identified. Here, we demonstrate that H3K9/36me3 lysine demethylase KDM4A/JMJD2A overexpression leads to localized copy gain of 1q12, 1q21, and Xq13.1 without global chromosome instability. KDM4A-amplified tumors have increased copy gains for these same regions. 1q12h copy gain occurs within a single cell cycle, requires S phase, and is not stable but is regenerated each cell division. Sites with increased copy number are rereplicated and have increased KDM4A, MCM, and DNA polymerase occupancy. Suv39h1/KMT1A or HP1γ overexpression suppresses the copy gain, whereas H3K9/K36 methylation interference promotes gain. Our results demonstrate that overexpression of a chromatin modifier results in site-specific copy gains. This begins to establish how copy number changes could originate during tumorigenesis and demonstrates that transient overexpression of specific chromatin modulators could promote these events.