I use PVGIS calculator to estimate photovoltaics energy gain to my satisfaction. It contains realistic Europe and Africa weather data.
Although this would be only a far estimate, let's assume you face south and you're based in Rome, Italy (instead of Chicago, IL), and we get:
- a maximum of 1260 kWh a year with an optimal inclination of 34° and almost south direction
- 810 kWh a year (64% short) with 90° inclination (straight up-down) and a south direction
from a 1 kWp installed power, i.e. 6m2 of fully covered area. As you probably don't want to entirely cover your windows, you should search for transparent thin film PV panels. Their covered area for 1 kWp would be double or more, depending on the required transmittance and price would be rather high (as of 2013).
Is this the best way? Sometimes it's better to consume less energy (or preserve more of it) than try to produce it.
Question Estimating the cost of solar panels and return timeEstimating the cost of solar panels and return time has got some very good answers with references of solar power generation calculators.