Chocobo breeding is a totally separate part of Final Fantasy, and to do it you need lots of Gil. Make sure you have these things:
Once you’ve got these things your ready to start your Chocobo Breeding. To rent out the stables go to the Chocobo Farm and go into the old cottage and ask the man, when he speaks to you, to look after your Chocobo’s for 10,000 Gil, then you’ll have a section of the stable where Chocobo Billy is. Keep doing this until you think you’ve got enough (Get Six anyway).