If you are willing to fly into San Jose, there are few direct non-stops available:
on 6/24
ORD SJC 0830 1052 AA2007 T7 738
on 6/28
SJC ORD 0615 1229 AA1722 T5 738
SJC ORD 1012 1622 AA1234 T6 738
Oakland has a number of flights available on 6/24 outbound and 6/28 return, BUT, AA does not fly direct to OAK from ORD, so you have to connect through Dallas.
Also if Midway is an option, you have more flights available. I also did find a direct SFO-ORD on 6/28, but it's early morning flight.
My point is this, AA will get you there, it may not be the exact flight you want, but after all it's an award ticket.
Call AA, you will find something if you are just a bit flexible.
Good Luck!
[This message has been edited by andrzej (edited Feb 09, 2004).]