The connection is
tight even if Finnair and AA (as your flights are marketed by Finnair but
operated by American, it's all Terminal 8, but Finnair would also arrive / depart here) share terminal 8 - if arriving from an international arrival, you must clear Immigration and Customs (retrieve your baggage at the carousel, pass through Customs and return your baggage to the counter just outside of Customs), and may have to pass through TSA security back airside any longer).
Domestic arrival connecting to domestic departure there are no formalities; domesitc to international you must show your passport as well as boarding pass on boarding.
The good thing is because these are
oneworld flights you will be protected onward; if you do happen to miss your connecting flight, AA will accommodate you on alternate flights with seat availability.
Also see:
JFK / New York Kennedy Connection & Times - Domestic & International (consolidated)
At Chicago O'Hare, you will merely arrive, walk to your connecting gate (assuming no delays on arrival) and when boarding they will check your passport and boarding pass. ORD can experience ATC holds and ground delays, etc. during summer (and winter); I prefer a minimum of two hours because of this.
We'll now move this to the AA Pre-Merger forum, as AA and US are not yet one airline.