They called yet again, and this time I decided to try for more info. The lady said the name of her company is "Power Choice" which, when Googled, appears to be in Australia. Why they are interested in electricity customers in Illinois, I have no idea.... Or, why they are using a Chicago number to call me.
A scam call. I didn't answer and they left no message. What's interesting is that a guy came to our door telling us he could save us money on both our electric and gas bills about two hours before this call. Others have indicated the people who answer this number (if you call back) say they are from an energy savings program company.
Best practice - never answer a call from a number you don't recognize. Let them leave a message; most often they won't.