The present invention relates to catalyst systems for preparing isotactic polyolefins obtainable by reacting at least one chiral transition metal compound and at least one cocatalyst which is able to convert the chiral transition metal compound into a cation, where the chiral transition metal compound contains two bidentate chelating ligands connected to one another via a bridge and, if desired, one or two further monodentate ligands, with the four coordinating atoms of the two chelating ligands being in an approximately planar arrangement around the transition metal ion 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 the trans position relative to one another, to the use of the catalyst systems of the present invention for preparing polyolefins, to a process for preparing polyolefins by polymerization or copolymerization of at least one olefin in the presence of one of the catalyst systems of the present invention, to the use of chiral transition metal compounds for preparing a catalyst system for the polymerization of olefins, to chiral transition metal compounds, to a process for preparing a catalyst system for olefin polymerization, to a process for preparing isotactic polyolefins, to polyolefins obtainable by a process according to the present invention, to polyolefin compositions comprising the polyolefins of the present invention and to products produced from such polyolefin compositions.