This invention is for a catalyst system comprising a neutral metallocene compound, an aluminum alkyl and a Lewis acid. The Lewis acid must be of sufficient acidity to ionize a neutral metallocene compound to form a cationic metallocene catalyst. The ligands of the Lewis acid should not be reactive with the metallocene cation. Any metallocene catalyst compound having two cyclopentadienyl rings attached to a transition metal would be useful in this invention. The invention is also for the process of using the catalyst system in polymerization of olefins. The metallocene is contacted with the Lewis acid. The aluminum alkyl is contacted with the olefin. The two mixtures are contacted with each other under polymerization conditions.