One of the reasons for failure of education system to form developed FL skills in its graduates consists in the lack of L2 immersion and low motivation of learners. Integration of Content and Language (CLIL) in teaching content subjects is believed to be an efficient way of improving the situation. However, introducing CLIL techniques and approaches can by itself pose a new great challenge for a university. Our study shows a stable interest in both students and teachers coupled with a high degree of doubts and lack of preparedness when it comes to the actual prospect of their involvement in CLIL courses. In addition, the introduction of CLIL requires systematic changes in academic and administrative policies of Russian universities. The authors suggest that in such environment, the optimal solution would be a gradual introduction of CLIL elements focusing elaborated preparatory techniques. The paper presents the design of pilot project of step-by-step introduction of CLIL format studies in a Russian university and summarizes the results of pre- and post-experimental surveys among university students and teachers revealing their expectations, causes for their uncertainty and showing the need for specific FL learning activities which form a support system provided by language teachers to boost learners' linguistic confidence. This introductory period calls for a special attention to the role of FL teachers and closer coordination of efforts between a content teacher and a language teacher.