As the Dark opposes the Light, so do the Lords of Chaos oppose the Lords of Order. Like the Lords of Order, Chaos Lord Imperators claim to serve beings that exist on a level far above even Imperators, outside Heaven and Hell and the World Ash, in the Lands Beyond Creation and beyond even them.
The goals of Chaos are frequently indistinguishable from those of the Execrucians. For all practical purposes, Chaos wants to destroy the universe -- as do the Execrucians. But Chaos claims it wishes to return creation to its natural state, one of raw, undefined, pure existence, unconstrained by thought or matter or energy. Defining creation weakens it; giving creation form renders it static and inflexible. Thus, they oppose the Execrucians, who want to erase creation as we know it.
Still, Chaos would like to unravel reality just as thoroughly as the Execrucians would, and the Lords of Chaos are almost universally regarded as enemies on Earth. (Almost universally because Lord Entropy himself has not declared them so, and the Chestnut Law applies to Chaos as it does to the Execrucians.) There are no Imperators of Chaos on Earth, but they have occasionally sent minions there, and a few human Nobles have taken up Chaos' cause.