Chicago is one of the big four Irish-American cities, along with New York, Boston, and Philadelphia. The city is located in Cook County and the Cook County Clerk of the Circuit Court oversees administration for that court system. In the 19th and 20th centuries, hundreds and thousands of people went through the naturalization process at their various courts.
Their website has an index of naturalization records from the late 1800s and early 1900s, as "the Clerk of the Circuit Court of Cook County Archives is home to more than 500,000 naturalization petitions covering the years 1871 to 1929. More than 400,000 of these records are Declarations of Intention, 1906-1929, which were usually the first papers to be filed by those who wished to become U.S. citizens."
This index is currently a work in progress but it is already showing tremendous promise for those looking for the Irish place of origin for their Chicago-area ancestors of this era. Currently, there are almost 7,500 index entries that list the county of origin for applicants. These numbers come from just six Irish counties: Clare, Cork, Galway, Kerry, Limerick, and Mayo. What is even better is that many of the index entries give details about what part of the county the applicant was born in. Overall, the index provides valuable information: name, birth date, birth town (this is where Irish place and county are to be found), birth country, and occupation.
It is useful to remember that someone did not have to live in Cook County, IL to declare their intent to naturalize. An immigrant could do so at any court. Therefore, don't discount those ancestors who lived in counties and areas around Cook County/Chicago.
You can access the database by clicking here.
If you find a relevant entry in the index you can apply for the declaration of intention via the application form at this link.
Number of records per county (as of July 2014)
Clare - 979
Cork - 753
Galway - 841
Kerry - 1261
Limerick - 986
Mayo - 2657
Total - 7477