If ppl dont know what to do:
1. Talk to Brutus at the Chocobo Stables Upper Jeuno (CS)
2. Choose: Release the Chocobo (CS)
3. Go to La Theine Plateau Position E-5 near the Ronfaure zone.
4. Examine the Chocobo Footsteppes and get a CS
5. Go back to Brutus at the Chocobo Stables Upper Jeuno
6. Talk with Brutus (CS)
7. Go to Southern San d'Oria Chocobo Stables and talk with the elvaan you saw in the last Brutus CS
8. Choose every option in the CS one time.
9. Go back to Upper Jeuno Chocobo Stables and talk with Brutus again (CS)
10. Wait 1 Real Life hour
11. Zone in and zone out when the 1 hour is over
12. Talk with Brutus (CS), after this you get a Chocobo Egg.
13. Go to your hometowns Chocobo Stables and trade the egg to one of the npcs, dunno wich exactly. Its one of the npcs you saw in the CS.
You completed the quest.
Now you can ask for all info on one of the npcs in the Chocobo Stable and watch how your egg/chocobo is doing atm on another npc.
Hope it helps a bit if you havent done the quest already :)
Thx Koalarampage (or something like that) for helping me out with the quest ^^