When chinchillas 'wag' their tails..

it means they are irritated!

I have always wondered why my chins 'wag' their tails sometimes.(Unlike dogs, their tails moved in horizontal motion, like sweeping the floor). After observing them for a period of time, I can conclude that they 'wag' their tails when they feel irritated(cats do that too).
Once, during playtime, for whatever reason, Oreo wagged his tail and started to chase Duffy allover the room,non-stop, ready to fight. Poor Duffy, he got tired and had to hide. They also wag their tails when I touch them too much(in their opinion) or when they hear some noises that they are sensitive to.