As soon as the main story has you join a Grand Company, there will be a sidequest available at your Grand Company headquarters called "My Little Chocobo". Take that quest. It will issue you a chocobo in exchange for 2,000 Grand Company Seals (which you can start earning once you join the GC).

GC Seals can be earned a wide variety of ways: FATEs, the GC hunting log, Duty Roulette, GC Levequests, Supply and Provision Missions, and a few other things, so even though 2,000 will seem like a lot at first, at least they accumulate fairly fast.