This is the link to the zoning map: http://maps.cityofchicago.org/website/zoning/liability.html
Thiss is the link to the zoning ordinance: http://www.amlegal.com/nxt/gateway.dll/Illinois/chicagozonin
The seller isn't required to produce a zoning cert on commercial property - only 1-4 unit residential properties. If the property is zoned commercial (which either B1 or B2 is) then I THOUGHT your financing would have to be at commercial rates and terms - which are not nearly as attractive as residential rates and terms. Hopefully your mortgage guy is knowledgable and knows what he's talking about?
Just so you know - B zoning is typically storefronts with apartments above them.
Hope that helps.
Should you not be able to procure financing as a result then you can try to back out of your contract via the financing contingency, you'd have to talk to your lawyer about your options here as this is a legal issue. However, if you try to back out for this reason, the seller generally has the right to find you financing at similar terms of your current arrangement with your lender. If the seller is able to do so, you still may be bound to the contract.
Long story short, clarify with your lender what the problem is and then consult with your attorney. In the future make sure that you realtor looks into issues like this before entering into a contract.