Good luck, Eagle! AMR is trying to take the cheap way out of a scheduling problem by violating your agreement and placing CHQ in your base. AMR could buy their way out of the CHQ contract, they could buy off Eagle pilots through pay/work rule increases, or they could just continue to operate those CHQ flights out of STL. AMR does not HAVE to put CHQ in ORD. Protect what you have, and make AMR pay what they already know they owe.
Someone earlier asked about the content of the CHQ/AA contract. While I know zero specifics, I would venture to say that there are no base-specific provisions in it. RAH has generally given their mainline partners a lot of latitude in terms of aircraft basing, as witnessed by our long history of closed bases and displaced pilots. Occasionally RAH requires a minimum amount of flying to be guaranteed into specific maintenance bases, in order to justify the investment in local staff, facilities, and equipment. For example, Republic is guaranteed a certain amount of flying out of PIT for US Airways, even though Airways has desperately wanted to reduce their PIT presence.