By chaotic, I mean a team, consisting of four or five players, with everyone playing different classes, that has chaotic features or randomness to it. If it doesn't exist that many, then just classes that can do a lot of different (potentially crazy) things. Also, how well would such a team composition do?

First classes that comes to mind is the wildmagic sorcerer and the wildmagic barbarian, but I'm not sure what other classes fit the description.

College of Creation Bard. The 6th level ability is really good for a creative person. Somebody in my party took it and frankly I'm scared. Imagine animating a rope, which most classes get as starter equipment, and then strangling someone on the battlefield? It can also fly, so if you want to get into somewhere high up you just command the rope to fly up, tie itself off on something, and then climb. You can also use the Performance of Creation feature to scam someone. Fun subclass .:)

Bard (College of lore) Ranger (Outlier, one of my homebrew subclasses) cleric, monk, rouge (I had this party once and everybody was unable to sit still the party was funny)

My go-to as a CoC bard was a canoe. I could ride through the air in it and beat people with it. But it really is fun to animate any random thing on the battlefield.

In terms of other chaotic classes, Wild Magic sorcerer goes without saying, and the magic barbarian sub is similarly weird and random. Trickster clerics, illusionist wizards.

Agree with scatterbraind on all points.