Component of heterochromatin. Recognizes and binds histone H3 tails methylated at 'Lys-9', leading to epigenetic repression. Interaction with lamin B receptor (LBR) can contribute to the association of the heterochromatin with the inner nuclear membrane. Homodimer (PubMed:10747027). Interacts directly with CHAF1A, EMSY, LBR, TIF1/TIF1A and TRIM28/TIF1B PXVXL motif via the chromoshadow domain (PubMed:8978696, PubMed:10562550, PubMed:10747027). Interacts directly with histone H3 methylated at 'Lys-9' via the chromo domain (PubMed:11571267). Interacts with SUV39H1, SETDB1, KMT5B and KMT5C (PubMed:10202156, PubMed:15145825). Interacts with PRDM6 (PubMed:16537907). Interacts with POGZ (By similarity). Interacts with CHAMP1 (By similarity). Interacts with INCENP (By similarity). Interacts with SGO1; the CBX1 homodimer binds to one molecule of SGO1 (By similarity). Interacts with LRIF1 (via PxVxL motif) (By similarity). Interacts with HDGFL2 (By similarity). Unassociated with chromosomes during mitosis. In all adult and embryonic tissues. Not phosphorylated. Ubiquitinated.