Just tried 1.11. I can't seem to put a chest on llamas, donkeys or mules. Tested on summoned and egged in (brother tested on natural mules) and no love. I tame them like normal with no problem. I can put a saddle on the mule or donkey and ride around, and carpet on the llama and llamas follow the lead llama alright, but can't put a chest on any of them, normally or spawning them in that way.

Single player. Server hasn't updated yet so I can't check it in multiplayer.