Those records are not open to the public. If you are sure they married in Chicago, you can print a request form for a marriage certificate at this website. http://www.cookctyclerk.com/records.htmlhttp://www.cookctyclerk.com/records.html They will only search thru 3 years for $7, and $1 for each additional year.They only have records for Cook County, and if they find no record, they will keep your money for a search fee.
If you are not sure whether they married in Chicago, but you know they married in IL, you can check with the IL Dept. of Public Health, in Springfield.They hold records for "all" IL counties.I do not know whether they will perform a search without an exact marriage date. http://www.vitalrec.com/il.htmlhttp://www.vitalrec.com/il.html
If you do not find the record in Illinois, I should also mention the fact that Crown Point, Indiana was a well-known marriage-mill in the 1920's.
You might ask your parent what church he or she, or their eldest sibling was baptized in.Perhaps that is the same church in which their parents (your grandparents) were married.Ask the church to search for the marriage record, a year or two before the birth of the first child.The church records will provide you with more info then the marriage license.You may find witnesses to the marriage, who may also be ancestors, and you may find godparents names on the baptismal records, who may also be related.