Involved in lipopolysaccharide (LPS) biosynthesis. Catalyzes the transfer of three 3-deoxy-D-manno-octulosonate (Kdo) residues from CMP-Kdo to lipid IV(A), the tetraacyldisaccharide-1,4'-bisphosphate precursor of lipid A. Thus generates the genus-specific LPS epitope of Chlamydia, composed of the trisaccharide alpha-Kdo-(2->8)-alpha-Kdo-(2->4)-alpha-Kdo