Do you have a copy of the marriage registration which might name his parents? They were married in St. Michael's Church in Chicago, and that parish register will likely have more info.
Name: Adam Schwartzkopf Age: 26 Gender: Male Birth Year: abt 1863 Marriage Type: Marriage Marriage Date: 26 Jun 1889 Marriage Place: Chicago, Cook, Illinois Spouse Name: Helena Sterkel Spouse Age: 22 Spouse Gender: Female FHL Film Number: 1030182
Even the witnesses to the marriage might provide more clues.
The 1900 census indicates he was born in Illinois? Ditto for the 1910 and 1920 census.
1870 US Census Chicago, Cook Co., Illinois
Dietz, Louis, aged 40, clerk in store, born Prussia Dietz, Elizabeth, aged 28, born Prussia Schwarzkopf, Peter, aged 9, attends school, born Illinois Schwarzkopf, Adam, aged 7, attends school, born Illinois Schwarzkopf, Elizabeth, aged 5, born Ilinois Dietz, Louis, aged 3, born Illinois Dietz, Emma, aged 6 months, born Illinois
This suggests a marriage for Elizabeth & Louis of about 1866, and the death of Adam's father not much before that. These are likely his parents in the 1860 US Census in Chicago:
Schwarzcap, Adam, aged 22, shoemaker, born Hesse(n) Schwarzcap, Elizabeth, aged18, born Hesse