Breeding Chocobos is a REALLY long process but it is so worth it. If you are planning on going after the two optional WEAPONs, then this is a must-do process. If not, it's still fun, and Knights of the Round is a fun summon for the really hard bosses like Proud Clod.
You can start raising Chocobos anytime after you get the Highwind. It's a good idea, though to wait till you get Cloud back because you need to be able to go to the Gold Saucer and race your birds.
Raising the Gold Chocobo
1. Go out, break stuff and make a LOT of gil. I mean a LOT. Like about 100,000 gil.
2. Go to the Chocobo Stables near Kalm and get all 6 of the stalls they will rent you. Talk to the guy in the house to rent them.
3. Equip someone in your party with the Chocobo Lure Materia, and take the Highwind to the tracks near Gold Saucer. Run around and catch 4 Chocobos, the max you can have in the pen at once. When you capture the Chocobo, jump off of it and the game will ask you what you want to do with it. Say "Send it back to the stable."
4. When you have 4 Chocobos, go back to the stable and talk to Choco Billy. He will be able to tell you the quality and gender of the birds. You want a "good' quality male and female and a "great" quality male and female, for a total of 4 birds. Let the others go.
If you are having problems finding the right Chocobos here, you can also try the tracks near Mideel (Or the hole that used to be Mideel)
5. Go to the North Continent and land on a grassy spot. Run around the grass until you fight a red dragon-looking enemy,. Steal from him till you get a 'Carob Nut'. Get 3 nuts, meaning you will have to fight 3 of these things.
6. SAVE YOUR GAME!
7. Talk to Choco Billy, and mate a MALE good with a FEMALE great or vice versa. Use the Carob Nut to mate them. You should get a green or a blue Chocobo from this mating. If not, reset the PSX till you get what you want. The Green and Blue need to be of OPPOSITE GENDER.
8. SAVE YOUR GAME!
9. Go to the Gold Saucer. If you don't have the Lifetime Pass, now is the time to buy it, so shell out the 30,000 gil. Race your new Chocobos to at least A Class.
If they need help, go out, make more money, and find the little house hidden in the hills on the North Continent. This is the home of the Chocobo Sage,and you can get greens from him. Reagan Greens are the best and you need at lest 15 or 30 of them to make a difference. **THE MORE GREENS YOU FEED THE BIRD AT ONCE THE MORE EFFECT THEY WILL HAVE**
10. SAVE YOUR GAME!
11. When they are A class, mate the Green and Blue Chocobos with a Carob Nut. You should get a Black Chocobo. If not, Reset and try again.
12. SAVE YOUR GAME!
13. Let all of your yellow, plain, Chocobos go. Keep only the Green, Blue and Black ones. Go up to the tracks in the snow near Icicle Village and capture four Chocobos. You need a Wonderful Chocobo that is of opposite gender of your black one. Keep it.
14. Go to Goblin Island, which is just of of the shore by Kalm. On the beach fight the Goblin and steal until you get a Zeio Nut from them. You can learn an Enemy Skill from them, too.
15. SAVE YOUR GAME!
16. Mate the Black and the Wonderful Chocobo together and you may or may not get the Gold Chocobo. If it doesn't give it to you after a few resets, get some more greens and race the birds to A Class.
16. When you get the Gold Chocobo ... SAVE YOUR GAME. Go get Knights. Kick some...
Other hints:
-- Higher-Class birds will give you better results. It depends on how patient you are. The first time I did this, I raced them all to A-Class. The second time I just did it and I got the green one off the bat. I am in the middle of testing how little you have to do right now.
-- This can take anywhere from 4-8 hours depending on how long you spend at the Races. If you are going to get Omnislash and Final Attack, I suggest you take GP for you prizes. You can rack up a lot this way.
-- Cid or Tifa may ask to ride. Let them, it doesn't matter and it's a nice change. (If you want to see it they have to be in your party.)
Good Luck!