Catalysis of the reaction: L-lysyl27-[histone H3] + 3 S-adenosyl-L-methionine = 3 H+ + N6,N6,N6-trimethyl-L-lysyl27-[histone H3] + 3 S-adenosyl-L-homocysteine. This reaction is the successive addition of three methyl groups to the unmethylated lysine residue at position 27 of histone H3, producing histone H3K27me3.