Remiem Temple. You must train a chocobo enough so that you can ride it around the Calm Lands (complete the first challenge sucessfully). Go to the south entrance, and take a right, until you see a Chocobo Feather. It will jump across, and you will be able to enter Remiem Temple. From there, talk to Belgemine inside the Temple, and defeat one of her Aeons.

It SHOULD drop the Aeon's Soul, but if not, the item itself is not necessary, since the improvement costs are VERY costly, unless you are playing a version where your characters have the Distills.