Chaos Gods are powerful and malevolent entities featured in Warhammer Fantasy as well as Warhammer 40,000 - in both versions they are the most powerful residents of the realm of Chaos: a parallel universe connected to our own but infinitely alien, the Chaos Gods are innumerable yet the most powerful of the legion are Khorne, Nurgle, Slaanesh and Tzeentch.
Chaos Gods can not enter the physical world but are omnipotent within their native realm, they can fashioned smaller versions of themselves (known as Greater Daemons) by which to visit the physical world but must always return to the realm of chaos as the physical world can not sustain them for long.
Due to this Chaos Gods are obsessed with corrupting the physical world so that they can absorb it into the realm of chaos and thus gain omnipotence over both realms - a feat that would spell certain doom for any sane creature or civilizations and a threat that has become a major part of both settings.
In the Warhammer Fantasy setting their main followers are the Hordes of Chaos while in Warhammer 40,000 they are served by the traitorous Chaos Space Marine legions - who broke away from regular humanity during what became known as the Horus Heresy.
The Horned Rat, patron deity of the evil-minded Skaven race, is often considered a Chaos God - though he is not confirmed (at least officially) as being a citizen of the realm of chaos: however given his alien nature, unthinkable power and former use of Greater Daemons it is quite likely he was a Chaos God (or at the very least an exceptionally powerful Daemon Prince).