The cheapest solution is a natural gas fired whole-house generator. About $5000 installed with automatic cut over.
Solar costs $10 to $20 per watt installed with controls. A typical house might need 5 to 10KWH average per day if you heat with some other fuel. A solar system that could support that would set you back $50,000 to $200,000. No way does the math work.
Solar costs are, at best, on par with residential energy costs. Their life is about 20 years, which is about the best case payback. Sadly, at best, solar works only when other sources are not practical (unless utility rebates help pay it down).
In Chicago, the number of clear days, the amount of snow that would block the panels, and the high latitude would all conspire against you too.
PS: Little known solar fact...if something partially shades your panel, say a shadow of a tree limb, that panel will quit producing, or will fall off way out of proportion with the % of shadow.