Rank 10+ chocobos and a "two hour" ability
I don't know if this has been mentioned but given that players are able to raise their chocobo under three different classes/jobs, and utilize those jobs in battle it would stand to reason that those same chocobos would be able to utilize an "ability" unique to that class. The downside is that these same abilities will have a drastically long "2hr" cool down between uses.
Healer Class - something akin to Benediction, that heals everyone in the party and removes most undesirable status effects
Tank Class - something akin to Invincible, but enhances both physical and magic defense but also increases enmity towards targets that have been placed on the "enmity list"
Damage Class - something akin to Blood weapon, that increases strength, speed and critical hit rate over a set period of time.
I also think this is something that should only be made available with rank 10+ chocobos.