It was a Lithuanian parish established in 1905 at 8801 S. Saginaw Street. Here is info about the church:http://www.neiu.edu/~reseller/cultinstp12.htm
My grandfather's nephew (his sister's son) was baptized in that church in 1913. His sister's family lived nearby about 5 blocks away. The Mormon Family History Center can order microfilm of the records for you to view.
Before the 1920 Census, Lithuania could not be recorded as someone's birthplace. Often they would recorded as being born in "Russia" or "Russia Poland" (usually this means the Suewalki/Suvalkija gubernia).
Because a Catholic Baptismal Certificate is accepted as legal proof just like a birth certificate, only records prior to December 13, 1915 are available
Parish Vol. Film # Film Item
St. Joseph Church Vol.s 1-3 1763437 items 1-9
These may have more data than what you found on-line.