Chicago lays out tentative timeline for COVID-19 vaccine distribution Jan 20, 2021 | coronavirus, Top Stories, Vaccination Chicago hopes to begin administering COVID-19 vaccinations to all eligible individuals by the end of May, according to a tentative plan unveiled Tuesday.To access this content, you must purchase 1 Year Health News Illinois Subscription or 1 Year Group Subscription - Up to 5 Users, or log in if you are a member.