I was referring to this thread: http://forums.eyesonff.com/showthread.php?t=45242

Talk to Chocobo Billy. One of the Options is 'Moving Chocobos'. He'll ask you to select which chocobo to move into the stable. You can inspect any chocobos you have out in the pen and he'll comment on the quality. If you select one, he'll prompt you to name the chocobo male or female.