Flights at this price are available starting from early September through November 7, 2018. Travel days vary but you'll have the best bet securing seats on Tuesday, Wednesday, and Saturday departures, but the odd Monday and Thursdays are also available.
This fare books into American Airline's basic economy but after September 5th, the airline will relax its stringent baggage policy and allow for a standard sized carry-on. If you still think that basic economy is too restrictive, you can book the same route on JetBlue for just $10 more roundtrip.
Searching on the AA site, I found seats departing BOS on Thursday, October 11 and returning from Monday, October 15, 2018. Seats are fairly wide open so you shouldn't have too much trouble finding an itinerary to match your travel needs.
Need a room in the Windy City? Take a look at what's available for the mentioned dates on Hotelwatchdog.