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 Su(var)205/HP1 to methylated histones. Mainly functions in heterochromatin regions; thereby playing a central role in the establishment of constitutive heterochromatin at pericentric regions. Involved in heterochromatic gene silencing including the modification of position-effect-variegation. {ECO:0000269|PubMed:14630943}.