When I wanted to be really obnoxious as a PC, my favorite alignment was Lawful Neutral. You may think Chaotic Neutral (sometimes known as Chaotic Retard) would be the most annoying alignment but you'd be wrong. Imagine all the arrogance and assholery of a Paladin preaching at you, but combined with none of the niceness and would drag you out of a burning building at the cost of his life part.
This is my experience with my players as well. It's why I can't wait until soon, when I get to be a player and I can roleplay a generic lawful good hero. I'm planning to be as annoying as possible to the evil douchebags the rest of my friends come up with.
One of my favourite PCs to date was created out of spite towards a couple of guys in my uni D&D group, who exclusively played Chaotic Bastard freakshit abominations with dead parents and eighteen-page backstories. I set out to create the ultimate foil -- a character so stuffy and unlikeable that he would prevent the campaign's otherwise inevitable descent into a Theatre Kid's Wet Dream by his mere existence.
The result: a Lawful Neutral human wizard with the Noble background, deemed too insufferable for even his old money parents and cast onto the streets to supervise a money laundering operation that the party was involved with. In practice, this meant acting like a tyrant and hurling racial epithets at the other PCs (to whom he was indispensable, being the only party member with enough money to bribe people). He was pathetically weak and had multiple medical conditions, because his family tree was a circle; to address this issue, I enlisted the help of one of the other players to create an ultra beefy fighter who would act as his bodyguard in battle scenarios, leaving him to stand at a distance and cast Magic Missile when the mood struck him.
The jokes practically wrote themselves. Any pretence of melodrama was quickly extinguished by His Majesty striding up to the villain and asking if they knew who his father was. Strangely, the others seemed to like him -- I think they thought I was doing some sort of pastiche of rich people.
About a dozen sessions deep, after we bluffed our way through a prison break with a few lucky Charisma rolls, our DM bequeathed upon us a disused ship powered by
magic, wink wink. When called upon to pilot the ship as the resident caster, he dismissed chauffeuring as "a Tiefling job" and locked himself in the captain's quarters. The rest of the party consisted of the aforementioned fighter, a barbarian, and two rogues. We spent the remainder of the session sailing the high seas at a blistering 1 mile per hour.
Shortly thereafter, the ship was hijacked by a gang of marauding goblins, and my wizard's bodyguard, having drunk himself into a stupor, was unable to save him. Goodnight, sweet prince. I shouldn't have given you 8 CON.