How to Find Chicago Church Records
The librarians at Newberry have put together THE guide to Chicago church records and so I will simply provide you a link to the PDF that they have published on their site. The Newberry Library Guide to Chicago Church and Synagogue Records.
Researching Catholic Records
If you're resesarching Catholic families, you should know that the records up through 1915 were microfilmed and they're available for browsing at FamilySearch.org.
The POINTers in Person website has the parishes listed alphabetically with information on address, founding dates, and ethnicity. Links for the parishes will take you to the corresponding entries in the Family History Library catlog.
The ChicagoAncestors.org website will let you see which parishes were closest to a particular address (make sure you convert street names and addresses, when needed) and this is particularly helpful if you're trying to determine where children might have been baptized. This website also includes information about when parishes were founded and provides Family History Library film numbers.
"Index" to St. Patrick's Marriages: The International Genealogical Index, available at www.familysearch.org, can serve as an index to at least some St. Patrick's marriages. To see the relevant entries, visit this page, select "North America" as the region and type in batch number M390564. Add a surname, if you wish, and then click on "search."
Priest/Parish Database
Have a marriage license with a priest's name, but no parish listed? Try searching the Priest/Parish Database.
At the moment, this database includes priest/parish entries from Chicago City
directories for 1874-75, 1879, 1885, 1890, 1896, and 1900. If you need other years, check a city directory.