Welcome to Flyertalk, Pierre-Laurent!

There are a couple of possible reasons - though I'm not sure which is correct:

1) That code is only valid on NEC (North East Corridor) Trains - which are generally routes along the east coast of the US. Chicago isn't along the east coast.

2) November 22 is close to Thanksgiving, which is November 28, so they may have that date as a blackout date.

You can use H431 & choose the AAA discount & pay with a credit card. For the date you're traveling, it drops the price down to $68.85 for a one-way best available fare. No one is going to ask to verify your AAA membership. The reason you should pay with a credit card (which you pretty much have to if you're buying tickets online) is because that way you can get your tickets printed out at the kiosk at the train station & never have to interact with anyone, thereby reducing your risk for having to have you AAA memberwship checked (which no one has ever done anyways). That's about the same price as 20% off of the lowest fare. If you're heart's not set on the train, there are one-way flights from MDW-LGA on American non-stops for $132.00 on the 22nd dependin on your schedule.