I read somewhere that chocobo breeding will come with housing.
I found it it was in the letter from the producer:

[39:53]
Q. Please tell us what we can do with individual player housing. Can we set our minions to play around the house? Can we make greenhouses and fields?
A. Through updates, we're planning to make it possible for players to grow gysahl greens and hatch baby chocobos and raise them. Also, we’re planning underground workshops where crafters can build boats and airships.

Link to letter from the producer