From Forgotten Realms Wiki

Chaotic evil is power without control, selfishness unfettered by any law.

A chaotic evil character does whatever his greed, hatred, and lust for destruction drive him to do. If he is simply out for whatever he can get, he is ruthless and brutal. If he is committed to the spread of evil and chaos, he is even worse. His plans are haphazard and any groups he joins or forms are poorly organized. Typically, chaotic evil people can be made to work together only by force, and their leader lasts only as long as he can thwart attempts to topple or assassinate him.

These characters will commit any act to further their own ends. Chaotic evil is sometimes called "demonic" because demons are the embodiment of chaotic evil.

Many serial killers would fit this description, as would indeed most of the more violent and reckless criminals found in the worst sorts of places.

[edit] Characters

Some characters in the Forgotten Realms setting identified as Chaotic Evil include:

Aznar Thrul
Dinin Do'Urden
Errtu
Halaster Blackcloak
Jhaartel Ealoeth
Klauth
Malice Do'Urden
Malik el Sami yn Nasser
Murial
Nalfein Do'Urden
Obould Many-Arrows

Non-canonical:
Edwin Odesseiron
Firkraag
Korgan Bloodaxe
Nizidramanii'yt
Shar-Teel
Simyaz
Thaxll'ssillyia
Tiax
(Bodhi, Sarevok, Tazok and Xzar are canonical characters whose non-canonical versions have been classified as Chaotic Evil.)

[edit] See Also

Alignment
Lawful good	Neutral good	Chaotic good
Lawful neutral	(True) neutral	Chaotic neutral
Lawful evil	Neutral evil	Chaotic evil