Oh and if you wanted to be first, there is apparently a much faster method. It involves the FATE Dark Devices in Northern Thanalan. Apparrently you can gain half a Chocobo level per Dark Devices FATE.

BUT! - And this is the reason why i have never done it - you must have a full group which includes your Chocobo, meaning you must be the party leader AND - here is the kicker - your group must be OK with a slot being taken up by your Chocobo. I have never done this as i think it would not be fair to the other group members to sacrifice a party slot for a pet.