Chocobo food can be obtained a number of various ways:

1)  Auction House:
go to Weapons -> Ammo & Misc ->
Pet Supplies.

2)  From Various NPCs:
The Stable Vendor NPCs in Windurst, Sandoria and Bastok sell Gysahl Greens, as well as the Chocobo Rental Vendor NPCs in Jeuno.

3)  Through some Caretaker Cutscenes:
Sometimes your Chocobo will find bits of food while you are taking it on either Short, Medium, or Long Walks with your Caretaker.
 
Your Chocobo may come across a Tokopekko Wildgrass, a Vomp or Zegham Carrot, a Gregorious Worm, or some other type of delicious goodie and this item will be
transferred to your inventory as long as your
inventory has free space.
 
If your inventory is full, don't fear.
Just free up an inventory space and check your Chocobo again.  Your item isn't lost and will then be given to you.

4)  From Gardening:
A large variety of Chocobo Food can be grown and harvested in your own Mog House.
For further information about gardening your
own Chocobo Grub, click Gardening in the
above menu or - Click Here -.

5)  Farming:
Some mobs drop Chocobo Food as well, so
farming particular items can alleviate some financial trouble.
 
Gausebit Wildgrass can be farmed off Wadi Hares in Dangruf Wadi, and Crane Flies in Meriphataud Mountains.

6)  From Bazaars
A lot of Chocobo Breeders garden as well,
and often bazaar their Greens and Carrots
in front of the Chocobo Stables in their home
town or virtually anywhere.
 
Reasonable prices for various Chocobo Items
on Fenrir are listed below.
[as of May 3rd, 2008]
Vomp Carrot:     700 - 1k each.
Zegham Carrot:  700 - 1k each.
Azouph Greens: 300 - 600 each.
Sharug Greens:  300 - 600 each.
Gysahl Greens:  50 - 100 each.
 
Keep in mind prices per stack are cheaper via
Auction House.  However purchasing from Bazaars are sometimes more convenient, sometimes the Auction House runs out of stock, and you can easily purchase items in the amount that you desire.

7)  From Racing NPCS
Every village has an NPC where you can race your Chocobo for Chocobo Bucks as well as overall Chocobo Racing Rank.

After placing in Races, you will receive a certain number of Chocobo Bucks which you can then exchange for Chocobo Food,
Racing Items, Chocobo Dye as well as advanced attribute packages.

 
For more information on Chocobo Racing and it's rewards, = Click Here =.