Unfortunately, it is nigh on impossible to say which three letter Xbox Live gamertags are still available, or indeed if any are available at all, due to the sheer number of possible three letter gamertags available.
Blurtit's highly scientific calculations put the amount of possible combinations of letters, symbols and numbers you could use to create a three letter gamertag around the 474,552 mark. That's four hundred and seventy four thousand, five hundred and fifty two! And a heck of a lot of possibilities.
So I Can't Have A Three Letter Gamertag?
All is not lost! When creating a gamertag for a new Xbox Live account you may be setting up, you can first try to put in the gamertag that you want. If this gamertag is not available, you will be given a list of suggestions similar to the gamertag that you want. I'm sure if you put in a three letter gamertag which wasn't not available, you would be presented with a list of similar three letter gamertags, and you can pick the best ones from there.