I live near O'Hare Airport in Illinois and I tried looking on the JAL site to possibly get an entry-level job with them. On the English site they don't have any mention of a career section, and I found something resembling one on the Japanese version but could only find corporate jobs in Japan... I think. Anybody here familiar with how to go about looking for something at the airport in this case?

Try calling them

Google

http://www.ar.jal.com/arl/region/en/other/career/

Am I an idiot for not trying Google? I mean it shouldn't be hard to find on their own website, right? Ugh.

it says no position available at this time.

They are hiring for entry level call center positions. Though it seems like the position is in CA so probably not what the OP is looking for.