At level 20ish, when you finish the story quests and finally pick a grand company, you then earn 2k grand company points via fates or whatever method you like and buy a chocobo pass you can then ride a chocobo as well as any mounts you get via CE or story (and at any level. At level 30 there is a quest in camp tranquil which allows you to do a short quest and get your chocobo buddy in your party.