One of my group mates has been quite obsessed with creating a Chuck Norris inspired character. He's playing a martial arts heavy, assassin flavors of Rogue, in a DnD campaign, which works well enough if we do heavy role-playing. I'm wondering, though, has anyone attempted to build a player character class which closely emulates the Chuck Norris internet meme (and, I guess, modified the surrounding game world to make sure that the game remains balanced enough to be fun to play)?
If you follow Penny Arcade at all, one of them (Gabe/Mike I think?) had a character called Jim Darkmagic. The whole premise behind him was that he was all talk/show, very little substance. Everyone knew him, everywhere, and he was famous, but he wasn't that amazing in reality.
For D&D, think lots of points in Charisma, and taking Intimidate/Bluff/Diplomacy skills, and lots of "method acting" - i.e. pretending to be the bad-ass that internet-chuck is pretended to be.
Other systems have other ways of modeling this. In GURPS you have reputation that you can purchase, for instance.
Another option is a Samurai Jack style character, who does very well at combat (not infallible!), and is well known because of his (in)famous attempts to bring down Aku.
Taking the question seriously, there are a number of interesting options here. First is the diceless Amber system which quite literally allows characters to bid in order to be best in the universes at... something. One of the rather awesome benefits of Amber is that you can have all of Chuck Norris' movies as backstory, having gone into different shadows and experienced them yourself.
In a more theoretical sense, it is absolutely possible to have a balanced game with the Chuck Norris meme: specifically the game should explore conflict other than combat. Allowing the player to explore how awesome he is in combat while framing the conflict above and beyond simple combat. If the player is interested, the conflicts could explore the "Violence really doesn't solve everything" trope.
If the player is quintessentially gamist (power-fantasy/fulfillment) and wants to achieve victory over all conflict in the game via a roundhouse kick, you have a rather more limited number of options as your social contract "I want a balanced game where failure is possible" is explicitly conflicting with his social contract "I want a win button." Here, unfortunately, the only way to resolve the conflict is discussion, compromise, or just walking away. One game that may fit that is Feng Shui, as that's functionally the genre that Chuck Norris popularized in the states.
The Internet meme suggests that Chuck Norris is a paragon of "toughness, attitude, virility, sophistication, and masculinity." He's practically unstoppable unless his own talents get in his way — the only one who can beat Chuck Norris is, essentially, Chuck Norris. Since this isn't a D&D specific question according to the tags, I'd look to Exalted to capture him, particularly a Dawn or Night caste Solar.
The Chuck Norris meme is entirely about reputation.
Were I building a CN character, I'd go with something like a monk (since they use martial arts), and then hope for a few places where the character is able to use a "Chuck Norris Roundhouse Kick (tm)" to drop a bad-guy. I'm thinking in early levels, if it's against some commoner who stole the donations for the festival of [fill in deity], and has little skill to fight back, but is able to be dropped by a couple of good kicks. After that, if everyone else is in on the joke, it can be a pretty short-term fun game/subplot.
I know it was with my ranger nicknamed "Kenny" because he had an uncanny ability to go into death's door every single combat. But be prepared for the player to get tired of the joke after a while, and want to replace that character.
The easy way is, as jeffszusz suggests, just ramp up the powerlevel of everyone else to match (it's the Meme action hero squad!). Presuming you're looking to run something of a more... normal level, I see two ways to approach it.
If you're running a point-buy system, Chuck just picks a couple areas that reinforce the meme (say, martial arts and intimidation/persuasion), and dumps all his points into it. He's going to be astoundingly good at kicking things and convincing people that he can kick them even harder. And that's all he'll be good at. (Which would tend to feed the mythos that Chuck solves his problems with a roundhouse, so it's not necessarily bad).
If you're playing a class-based, you can do the above to a lesser extent, and fill in the blanks with a bit more hand-waving and roleplaying. (Maybe a roundhouse kick is just a Monk with Cleave).
In all cases, it comes down to the player - does he want to play Chuck because he thinks the concept is funny, or because he's angling for power-gamer?
It's all about letting the other players do something over-the-top and picking a system that will allow it.
If someone wants to be Chuck Norris, he's going to be in a world where other PC's are the action-hero-personas of Vin Diesel, Clint Eastwood, Arnold, Bruce Willis, etc.