The Newberry Library is an independent research facility founded in Chicago in 1887. Since that time there has been a focus on collecting genealogy and local history publications. Today, there is a dedicated part of the library for these topics. Chicago area Townland of Origin readers will be pleased to see that the library has general Irish collections and specific Irish genealogy collections.
Some items of note include:
19th century newspapers and journals from Ireland
Irish newspapers from Boston and New York
Pettigrew and Oulton’s Dublin Almanac (1834-1848)
A large range of local history publication from Ireland
Irish genealogy reference and 'how to' books
Publications about Irish immigrants communities in the U.S.
All in all, it seems like a very good place to conduct Irish genealogical research in Chicago.