Instructions
Play through the game until the party takes control of the airship called the Highwind and can fly it freely around the world.
Land the airship near the city of Kalm and go into the chocobo farm nearby. Speak to the owner, Choco Bill, and rent out several sets of stables.
Hop back into the airship and fly to the home of the Chocobo Sage to the north of Icicle Inn. Buy several Reagan greens from the Sage and then equip the "Chocobo Lure" materia on any of your party members.
Fly over to the area near Gold Saucer. Land the airship and walk on the chocobo tracks found there until the party is attacked by a chocobo with two other monsters in front of it. Use the Reagan greens on the chocobo and then kill the monsters. After the battle, send the chocobo back to the stables you rented. Repeat this process a second time, walking on the tracks again and capturing another chocobo.
Leave Gold Saucer and land the airship near the city of Mideel. Complete the same process as before, capturing two different chocobos on the tracks near the city.
Take a trip on the airship to the town called Bone Village and fight the monsters outside until the party runs into a creature called a Vlakorados. Use the "Steal" materia on the Vlakorados to steal two items called "carob nuts" from the creature.
Return to the chocobo farm and breed your two sets of chocobo together. When Choco Bill asks if you want to use any items, choose to use both of the carob nuts. After the breeding is finished, a green and blue chocobo will be produced.