Heterochromatic domains of DNA account for a large fraction of mammalian genomes and play critical roles in silencing transposons and genes, but the mechanisms that establish and maintain these domains are not fully understood. Here, we use a CRISPR-based genetic screen to investigate the requirements for establishment and maintenance of histone H3 lysine 9 trimethylation (H3K9me3) heterochromatin. In mouse embryonic stem cells (mESCs), we show that transiently induced H3K9me3 heterochromatin is inherited for a limited number of cell divisions, independently of sequence-dependent recruitment, but becomes stable upon differentiation, concomitant with downregulation of enzymes erasing H3K9me and DNA methylation. In addition, ordered and non-redundant activities of multiple H3K9 and DNA methyltransferases, together with histone deacetylases, chromatin remodeling complexes, and RNA processing factors, are required for heterochromatin maintenance. Our findings suggest that a newly acquired H3K9me3 domain can be maintained like an imprint but requires reinforcement by DNA methylation and other pathways.