Well, Paladins are lawful, because among other things they're pretty strict about following a certain code.
You can't do that with a chaotic character. They're a lot more about doing what the heck they just feel like.
Mind you chaotic does not mean "has to do everything against the law" because that's just following a code too. A code that happens to be opposite of the other code, but still practically a code.
As Quatar implied earlier, the Paladin is a Champion of Good, not Law or any thing else. The reason for the LG requirement is that anyone who unfailingly holds to a code of conduct is Lawful. Hence, no CG paladins.
I would suggest reading the Complete Paladin's Handbook by Rick Swan (TSR, 1994).
What better nemesis for a paladin than his direct opposite, an “anti-paladin” that embodies the forces of evil? As the mirror image of a normal paladin, an anti-paladin might be able to detect the presence of good, generate a aura of protection against good creatures, and wield an “unholy” sword.
Though DMs may experiment with any type of character they like, we discourage the use of antipaladins. Good and evil are not merely mirror images of each other. Just as the forces of evil have their unique champions, the paladin is intended as a unique champion of good. The paladin originates from a tradition of dynamic balance, in which the forces of good are few and elite and in which forces of evil are numerous and of lesser quality.
Allowing anti-paladins blurs this basic relationship."
I won't quote any more of the book here, but for anyone interested in flavour for their Paladins, this book is a treasure.