Histone methyltransferase that specifically trimethylates 'Lys-9' of histone H3 using monomethylated H3 'Lys-9' as substrate. H3 'Lys-9' trimethylation represents a specific tag for epigenetic transcriptional repression by recruiting HP1 (CBX1, CBX3 and/or CBX5) proteins to methylated histones. Mainly functions in heterochromatin regions, thereby playing a central role in the establishment of constitutive heterochromatin at pericentric and telomere regions. H3 'Lys-9' trimethylation is also required to direct DNA methylation at pericentric repeats. SUV39H1 is targeted to histone H3 via its interaction with RB1 and is involved in many processes, such as regulation of organ-specific terminal differentiation during development. N(6)-methyl-L-lysyl(9)-[histone H3] + S-adenosyl-L-methionine = H(+) + N(6),N(6)-dimethyl-L-lysyl(9)-[histone H3] + S-adenosyl-L-homocysteine N(6),N(6)-dimethyl-L-lysyl(9)-[histone H3] + S-adenosyl-L-methionine = H(+) + N(6),N(6),N(6)-trimethyl-L-lysyl(9)-[histone H3] + S-adenosyl-L-homocysteine Associates with centromeric constitutive heterochromatin. Expressed ubuitiously. Expressed both maternally and zygotically. Although the SET domain contains the active site of enzymatic activity, both pre-SET and post-SET domains are required for methyltransferase activity. The SET domain also participates in stable binding to heterochromatin (By similarity). In the pre-SET domain, Cys residues bind 3 zinc ions that are arranged in a triangular cluster; some of these Cys residues contribute to the binding of two zinc ions within the cluster. Belongs to the class V-like SAM-binding methyltransferase superfamily. Histone-lysine methyltransferase family. Suvar3-9 subfamily.