Hi Beth-
All of the information came from a combination of Cook County Government websites (all on-line information):
Cook County Assessor's Office
" " Treasurer's Office
" " Recorder of Deeds Office

As to the question about your gggrandfather's business...
Although I have never done it for a property that far back, my guess would be the answer is "yes" and I don't think you will need a DOB.
The Recorder of Deeds office maintains a Grantee/Grantor index by name. I don't know how far back it goes, but it is available on-line back to 1985. You'll have to check with them to see how far back their records go at their office.
Assuming your ancestor made any property transfers at all, there should be a record of it there. It might be kinda difficult to locate if your ancestor had a common name (Cook County is and was a BIG place). You will also have to have a given time frame in mind to narrow down your search. You must also remember that if and when you do locate a record it might not indicate it was "Joe's Grocery Store" but will be presented as a legal description of the property and the type of document maintained in their files.

Hope this helps.
Good Luck in your search.
Paul