Blue Cross and Blue Shield of Illinois announces third neighborhood center in Chicago Mar 6, 2020 | Home Health, Long Term Care, Top Stories Blue Cross and Blue Shield of Illinois plan to open their third Blue Door Neighborhood Center on Chicago’s west side, the company announced Friday.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.