Inasmuch as there is zero cost or obligation I don't see any benefit to closing the account, but you can send a request to this address or fax number:
American Airlines AAdvantage Department, P.O. Box 619688, DFW Airport, TX 75261-9688
... or Fax to +1-817-963-7882.
I'm having mixed thoughts now.. I think I might keep it and I still want to donate some money to Unicef so I can get the AAdvantage card. When I try to donate, it lets me choose my country of residence-Australia, but won't take my card!? It says that there has been an error. I have contacted the card issuer and they say that they are not having any problems, the transactions don't even show up!? Can anybody please help?