It's hard to give an answer without knowing more details.
Introducing a new race like this has several points of potential problems.
1) Unbalanced mechanics. The statistics of the race may be too powerful, too weak or too strange to work properly within a standard D&D game.
The two solutions are to get someone who knows the system well (yourself, another player or the enworld house rules forum) to take a look over it and see if they think there'll be any problems.
Or alternatively offer to take the ideas and themes of the race they want, but to construct the mechanics yourself (possibly with the help of the enworld house rules forum again).
2) Disruptive for the setting. If you're running a very detailed setting already, either homebrewed or published, then it may disrupt the setting to suddenly add an island of demonic gorillas.
3) Extra work. Let's face it, you're already giving up a lot of your time and effort to make a game everyone can enjoy. If it will take up more work than you're happy to contribute to include this in the game, it's quite fair to say you can't afford the extra time to make this work.
4) Make the other players unhappy. If the players feel cheated 'Why should he get to play something special', then they may get annoyed by this player getting a special race. Or alternatively they may want to do the same thing too. Maybe that's fine, but four people doing this can compound the above three problems and make things worse than just one person.
So if those 4 problem can be solved, or don't apply, then sure. Why not. But if you think those may create problems, you're well within your rights to say "No, not this time".