There is one question I keep repeating every time someone asks about finding details about their family: "Do you have church record of their marriage?"
If your ancestor immigrated to U.S. and married in U.S., you usually have marriage license from official authorities in the County your ancestors lived in. BUT - these marriage licenses contain just a little information when compared to the church records. You have a name there, but not much more. Here are two examples of marriage licenses (as found through Google):
So what we know from these licenses? Honestly, almost nothing. Now, what about church records? Those are usually not available online so you'll have to ask the church where your ancestors were married if they can provide a copy of such record to you. It takes time, it could even mean you'll have to go there and ask personally, but believe me, it's worth it.
Anyway, if your ancestors came to Chicago and were married in St Procopius church, maybe you'll be the lucky one to find their church marriage record online on FamilySearch website. And here is one example from 1909:
I know it's complicated because it's in Latin, but it won't stop someone who is researching his family history, right? So, what do we have here? Groom Václav (Wenceslaus) Vocásek, originally from Radovesnice in Bohemia, born on 27th Nov 1874, son of Václav (Wenceslaus) Vocásek. Bride Josefa Mačlová, originally from Strakonice, born there on 14th March 1885, daughter of Václav (Wenceslaus) Mačl.
Now we know where both groom and bride were born - and also when, so it's just a matter of time to find their birth records. This is not the information you would receive from the marriage license, right?
So - don't forget church records, they will provide you much more information than the civil ones... :)