With this paper we try to contribute to the debate on the nature of research intensive universities and the chances to create this type of institution in Poland. Research universities are presented as elite, flagship institutions for educating students mostly at the doctoral level and to produce the bulk of the research output. Examples of world-class research intensive universities from various countries are presented. It is shown that intensified competition among universities exists to prove their performance through global university league tables or ranking exercises and it is discussed whether Poland is at the stage to create at least one such institution playing important role in that competition. We argue that the establishment of a University of the Polish Academy of Sciences could be a solution. This University stands to become a unique research institution in Poland and one of very few establishments of its type in Central and Eastern Europe. The University will conduct scientific research and provide programs of the highest standard, exploiting the research and teaching potential of the PAS institutes as well as the competence and experience of members of the Academy's corporation. It is intended as a higher education institution with a decentralized organizational structure, based on the PAS research institutes. The University of the Polish Academy of Sciences will have a quality-boosting impact on the PAS institutes as well as initiate their consolidation and reorganization in the field of teaching.