Genocide is from the 1996 Chaos! comics miniseries "Lady Death: The Crucible", and has appeared in several other Chaos! series since. He is one of the Chaos Lords (along with Jehovah,Lucifer,Odin,Armageddon,Brahma,Kreator),the ancient beings who created the modern universe from primordial Chaos on accident, and he seeks to return it to primordial chaos.
Genocide's early life is mostly unkown, but he has stated that Lucifer is his younger brother, and it has been stated by narration that he was perfectly content with the universe as it once was,:totally chaotic with nothing defined as seperate from anything else.
At one point he married Antigone and had a two children named Vex and Scorpia.
He later had a daughter named Sinestra. He also became king of his own planet,Wraithworld,from which he lead a massive empire of wraiths who possessed similar nihilistic desires.
Quest to Destroy the Universe
Genocide went on a quest to find any power source that could destroy the universe, and eventually found one in Odin, King of Asgard. Genocide did manage to kill Odin, but Odin was able to hide his power before Genocide could access it. Genocide attempted to conquer Asgard, but was met with heavy resistance by the Aesir and Lady Death, who raised all of the dead in Asgard in order to create an army against Genocide.
Genocide found the Odin Power,and brought it back to Wraithworld,but Lady Death was able to kill him before he could destroy the universe (though he did manage to destroy a few stars). Later on Genocide, in typical comic book fashion, returned from the dead and again attempted to do what he was planning before he died.
He was still stopped, however.