Catalysis of the reaction: L-lysyl9- + 3 S-adenosyl-L-methionine = 3 H+ + N6,N6,N6-trimethyl-L-lysyl9- + 3 S-adenosyl-L-homocysteine. This reaction is the successive addition of three methyl groups to the unmethylated lysine residue at position 9 of histone H3, producing histone H3K9me3.
histone H3K9 trimethylation