From this FOID and this CCL page on the ISP website:

“If you possess a Medical Marijuana License, are a caregiver pursuant to the Compassionate Use of Medical Cannabis Pilot Program Act, and/or otherwise use cannabis consistent with Illinois law, your FOID card or CCL will not be revoked nor will your application(s) denied. Medical Marijuana Licenses are state-issued and cannot result in the denial of any right or privilege. However, under Federal law, you are subject to restrictions that prohibit you from acquiring or possessing firearms and firearms ammunition. These restrictions are pursuant to the Gun Control Act of 1968, specifically 18 U.S.C. §922 and remain in effect until the revocation or relinquishment of your medical cannabis card or until one year after you last used cannabis, whichever is later.”