According to Wikipedia, Eris (Greek Ἒρις, "Strife") is the goddess personifying that quality, her name being translated into Latin as Discordia. Her Greek opposite is Harmonia, whose Latin counterpart is Concordia.

Encyclopedia Mythica says of Eris: "Eris is the Greek goddess of discord and strife. She is Ares' constant companion and follows him everywhere. Eris is sinister and mean, and her greatest joy is to make trouble. She has a golden apple that is so bright and shiny everybody wants to have it. When she throws it among friends, their friendship come to a rapid end. When she throws it among enemies, war breaks out, for the golden apple of Eris is the Apple of Discord. She did this once during the wedding of Peleus and Thetis, and this act brought about the Trojan War."

Wikipedia continues:

The most famous tale of Eris ('Strife') recounts her initiating the Trojan War. The goddesses Hera, Athena and Aphrodite had been invited along with the rest of Olympus to the forced wedding of Peleus and Thetis, who would become the parents of Achilles, but Eris had been snubbed because of her troublemaking inclinations.

She therefore (in a fragment from the Kypria as part of a plan hatched by Zeus and Themis) tossed into the party the Apple of Discord, a golden apple inscribed Kallisti — "For the most beautiful one," or "To the Prettiest One" — provoking the goddesses to begin quarreling about the appropriate recipient. The hapless Paris, Prince of Troy, was appointed to select the most beautiful. Greek mythological morality being what it was, each of the three goddesses immediately attempted to bribe Paris to choose her. Hera offered political power; Athena promised skill in battle; and Aphrodite tempted him with the most beautiful woman in the world: Helen, wife of Menelaus of Sparta. Paris was a red-blooded young man, and while the length of time he meditated on this problem is not recorded, he did eventually award the apple to Aphrodite.

Modern Discordians hail Eris as their matron deity. Principia Discordia, their Holy Book, tells more of Eris:

What We Know About ERIS (not much)

The Romans left a likeness of Her for posterity — She was shown as a grotesque woman with a pale and ghastly look, Her eyes afire, Her garment ripped and torn, and as concealing a dagger in Her Bosom. Actually, most women look pale and ghastly when concealing a chilly dagger in their bosoms.

Her geneology is from the Greeks and is utterly confused. Either She was the twin of Ares and the daughter of Zeus and Hera; or She was the daughter of Nyx, goddess of night (who was either the daughter or wife of Chaos, or both), and Nyx's brother, Erebus, and whose brothers and sisters include Death, Doom, Mockery, and Friendship. And that She begat Forgetfullness, Quarrels, Lies, and a bunch of gods and goddesses like that.

One day Mal-2 consulted his Pineal Gland* and asked Eris if She really created all of those terrible things. She told him that She had always liked the Old Greeks, but that they cannot be trusted with historic matters. "They were," She added, "victims of indigestion, you know."

Suffice it to say that Eris is not hateful or malicious. But She is mischievous, and does get a little bitchy at times.

*THE PINEAL GLAND is where each and every one of us can talk to Eris. If you have trouble activating your Pineal, then try the appendix which does almost as well. Reference: DOGMA I, METAPHYSICS #3, "The Indoctrine of the Pineal Gland"

DIRUIT AEDIFICAT MUTAT QUADRATA ROTUNDUS

— Horace

The story of Eris being snubbed and indirectly starting the Trojan War is recorded in the Principia, and is referred to as the Original Snub.

Eris | Discordia | Robert Anton Wilson

Adoration of Eris artwork by GrouchoGandhi.com