This is the best walkthrough on Chocobo breeding that you will ever read. I will explain only what you need to do and will not go off telling you about every kind of nut there is, and stuff like that. You will need a lot of gil. Probably about 400 thousand. (I'm not kidding) It will also take you about four to five hours, maybe more, mainly because of the racing. That takes about 80-85% of your time. So I don't have to explain this later on, here are some tips for racing your Chocobo's.
Ok, first of all to win the races you need to feed your chocobo's about 11 Sylkis Greens. You can buy these from the Chocobo Sensei located on the northern continent, (The Snowy One). After you feed your Chocobo, the greens head over to the Gold Saucer. Oh yeah, I forgot to tell you. You absolutely need to by a Gold Ticket! It's a lifetime pass to the Gold Saucer. You can buy one from the girl outside the Gold Saucer for 30,000 gil. Believe me it's a good deal. Now go to the Chocobo Square and talk to Ester, the girl on the far-left side of the screen. When she asks you if you want to race on a long or short course, always say you want the short one. Now when you are in the race press the select button on your control pad to switch to manual mode. Now here are the tricks:
Hold R1, R2 and square at the same time. This makes you go faster and your stamina will not decrease.
Hold R1, R2, L1 and L2 at the same time. This makes your stamina go up.
That's about it for the tricks. If you use those, you are sure to win. Although there is a LITTLE bit of skill involved. Now that's it for the racing tips.
Note: That is not the first part of the walkthrough. That is only to be used when you have a chocobo you want to keep and it's time to race.
Now, the first thing you want to do is equip the Chocobo Lure on one of your guys, then rent six stables at the Chocobo farm. Now the first Chocobo you want to get is a male walking Chocobo. You can find these around the Gold Saucer area near the water. You should always capture four Chocobo's before going back to the Chocobo Farm. When you catch four, return to the farm. Talk to Choco Billy and tell him you want to move Chocobo's. He will give you a rating of how good your Chocobo is. The only Chocobo's that are good for anything are the Great and Wonderful Chocobo's. So you should look through your four Chocobo's and find one that says " This is a great Chocobo. If you don't have any great Chocobo's, or the only great Chocobo you have is female, then go get four more from the same spot where I told you to go before. Once you have found a male great Chocobo, you should race him until he is at the S Class. When he is in the S Class then go south near Mideel. Here you can catch a female running Chocobo. Once you have caught a running female great chocobo, then race her to the S Class. (You need to race all Chocobo's to the S Class always) Now mate the two Chocobo's with the Carob Nut. You can steal the Carob Nut from a red dragon in the green area by the Chocobo Sensei's house. (You should steal about 3 Carob Nut's. You will need them later on) You should get either a green or blue Chocobo. If you don't, which should not happen if you did everything right, just reset the game and try again. It does not matter which is male or female anymore so whatever kind of blue or green Chocobo you get is good.
I don't think you can breed your two yellow Chocobo's again, so you need to repeat the process to get the same Chocobo's. If you don't know what I mean, you need to get a male walking great Chocobo and a female running great Chocobo and breed them. This time try to get the opposite of what you got before. For example if you got a male blue Chocobo the first time, then you should try to get female green Chocobo. Now that you have a green and blue Chocobo, race them to until they are S Class. Then breed them with the Carob Nut. You should get the black Chocobo. By the way if you are running out of room in the stalls, then you can release all of your yellow Chocobo's.
If you got a female black Chocobo then you need to find a male dashing wonderful Chocobo. You can find these on the northern continent, in the West Side near the ocean. As always, catch four of them and go back to the farm. When you are picking out which Chocobo you want to move into the stables, Choco Billy should say "This is a wonderful chocobo." Now that you have your dashing chocobo, you need to race him/her and the black chocobo to the S Class. Now you need to go to the islands on the right side of the world map and steal the Zeio Nut. You can steal the Zeio Nut from some little goblins on of the islands. I think that they are in the forest. Now that you have the Zeio Nut, go back and breed the black Chocobo and the dashing Chocobo with the nut. Congratulations! You have the GOLD CHOCOBO!!!!!!!!!!!!!!!!!
* Credits to Pumbert for writing this.