The Fat Chocobo is another Final Fantasy trademark. They are an extremely fat and multi-stomached Chocobo that is also quite intelligent. By using a certain veggie from the town of Gisahl (Carrot), which happens to be this chubby chocobo's favorite food, the Fat Chocobo will suddenly appear (boy is he hungry!) and will deposit any items you do not need immediatedly in his stomach. He most likely needs the items as something to digest his food with, but luckily, your items are unaffected even after long stays. However, he cannot swallow special items (or plot items).
The Chocobo appears in any forest by dropping a carrot where 'It smells like Chocobo's', or in the 'Invincible', where you can also by vending machine carrots.