Instructions
Purchase Chocobo lure. Choco Bill's Chocobo Ranch sells Chocobo lure Materia for 2,000 GIL. However, if you talk to a Chocobo in the stable the first time you visit the ranch, the Chocobo sometimes gives out the lure for free. Equip the materia.
Buy greens from Choco Bill. Chocobos like to eat greens, so you will need them when you encounter them in the wild. Greens come in several different varieties, but Tantal greens work well.
Look in the right area. For a great Chocobo, search the area around Mideel. When you find bird tracks, walk over them until you are engaged in battle with a Chocobo.
Give the Chocobo the greens. Do not attack the Chocobo and scare it off. If bad guys accompany the Chocobo, fight them, but keep the Chocobo distracted during the entire battle by continuing to feed it. Make sure not to use an attack, such as lightning, that hits all enemies. When the battle ends, the Chocobo is yours.
Show your Chocobo to Choco Bill. He will tell you the Chocobo's class. If it isn't a great Chocobo, start searching again.