Upvote:2
Step by Step instructions for international arrival: https://www.flychicago.com/ohare/myflight/international/pages/default.aspx
Step by Step transfer guide: https://www.flychicago.com/SiteCollectionDocuments/O%27Hare/MyFlight/TransferGuide.pdf
It's a tight connection and hard to predict. It really depends on how much time you will need to get through immigration, get your bags and through customs.
The good news: it's a single ticket and hence a "legal" connection. If you miss your flight BA (or their US domestic partner) will re-book on the next available flight for free. Assuming it's American Airlines (One World Partner for BA), there are 5 non-stops a day with the latest one leaving at 9:38pm