The Key of Hate is required to open the first red portals in the Pandemonium Event and can only be found from certain boss monsters, and only on Hell difficulty.
Get the Key of Terror from The Countess, the Key of Hate from The Summoner, and the Key of Destruction from Nihlathak. It's a good idea to have 3 of each key before beginning the second stage of the Pandemonium Event, for reasons explained in the Pandemonium Event article.
The keys look identical, and can only be discerned between by hovering on them to see their name.
Key of Hate
The Summoner drops this one. He's found at the end of one of the four points of the Arcane Sanctuary, in Act Two. He will only drop a Key of Hate on Hell difficulty, and even then only every few games.