Chicago, Cook Co. Naturalization Records from Superior, Circuit, County and Criminal Courts (1871-1929)
I can search the microfilmed index for your ancestor and provide a digital copy of the actual naturalization papers available from the Cook County Courthouse, Chicago, Illinois.
If you found an entry in the on-line Cook County Clerk of the Circuit Court database, http://www.cookcountyclerkofcourt.org/NR/about.aspx I will only be able to obtain the Declaration, which will not include any more information than what is in the database.
If you found an index card in the www.ancestry.com database, that Naturalization may provide good genealogical information if your ancestor was naturalized after 1906, (although some 1904-1906 naturalizations have good information also). If the index card states “court order only”, most likely there will only be one page for his naturalization and won’t include much significant information.