I think I know the answer to that one, but someone correct me if I'm wrong...

When you've dispatched at least 3 chocobos at each of the 5 levels, and they all return, a secret dungeon opens in the ranch. Inside the dungeon are 5 gates; if you can navigate your way through the dungeon and open all the gates, you'll get the Awesome Chocobo. There are a lot of tough fiends in this area, but there's also some key items, including an Experiment Repair Manual and the Machina Reactor (for Rikku's Machina Maw Dressphere).