In most non-criminal or "civil" cases, you usually do not have the right to a free lawyer. However, there are many legal aid and pro bono programs that provide free legal help if you meet their income and other eligibility criteria.
If you are looking for free legal help in Chicago or Cook County, in most cases, the best place to start is by calling the CARPLS Legal Aid Hotline at (312) 738-9200. The hotline is staffed by lawyers who can give you free legal advice by phone. If there is a free legal aid or pro bono organization that may be able to offer more help, the CARPLS lawyers will tell you who else to call. You may be apply for free legal help online at Illinois Legal Aid Online (ILAO).
You can learn more about free and affordable legal help in the Chicago area in the Free and Affordable Legal Help in the Chicago Area guide.