It is not impossible. Apply. You might be denied but you will be entitled to appeal the denial . Depending upon the nature of your juvenile conviction, how long ago it was, your lifestyle now, etc. you might be able to secure a FOID card. You could also speak to an officer in charge at the ISP office that handles FOID cards - 217-782-7980 between 8:30 a.m. and 5:00 p.m. Don't bother speaking just to clerical staff. Best wishes.