Linkage-specific ubiquitin chains govern the outcome of numerous critical ubiquitin-dependent signaling processes. However, the targets and functional impacts of linkage-specific ubiquitin modifications remain incompletely understood, due to a paucity of tools for their specific detection and manipulation. Here, we applied a cell-based ubiquitin replacement strategy enabling targeted conditional abrogation of each of the seven lysine-based ubiquitin linkages in human cells to profile system-wide impacts of disabling formation of individual chain types. This revealed proteins and processes regulated by each of these poly-ubiquitin topologies and established indispensable roles of K48-, K63- and K27-linkages, but not K6-, K11-, K29- and K33-linkages, in cell proliferation. We show that K29-linked ubiquitylation is strongly associated with chromosome biology, and that the H3K9me3 methyltransferase SUV39H1 is a prominent cellular target of this modification. K29-linked ubiquitylation catalyzed by TRIP12 and reversed by TRABID constitutes the essential degradation signal for SUV39H1 and is primed and extended by Cullin-RING ubiquitin ligase activity. Preventing K29-linked ubiquitylation-mediated control of SUV39H1 stability deregulates H3K9me3 homeostasis but not other histone modifications. Collectively, these data resources illuminate cellular functions of linkage-specific ubiquitin chains and establish a key role of K29-linked ubiquitylation in epigenome integrity.