The present invention relates to catalyst systems for preparing isotactic polyolefins which are obtained by reacting at least one chiral coordination compound of a main group element selected from the group of elements consisting of Al, Si, P, S, Ga, Ge, As, Se, In, Sn, Sb, Te, TI, Pb, Bi and Po as central atom and at least one cocatalyst which is able to convert the chiral coordination compound into a species which displays polymerization activity toward at least one olefin, with the chiral coordination compound comprising two bidentate chelating ligands joined to one another via a bridge and, optionally, one or two further monodentate ligands and with the four coordinating atoms of the two chelating ligands surrounding the main group element as central atom of the coordination compound in an approximately planar fashion and up to two further ligands being located above and below this approximately planar coordination sphere formed by the four coordinating atoms of the two chelating ligands and, in the case of two such further ligands, these being in trans positions relative to one another.