I don't think their is anything really wrong with it, as long as you make sure to limit the time he plays. Some people can get kinda "obsessed" when their older and some just don't.
To me it does seem a little odd for a three year old to play w/an Xbox360, but I started playing computer games when I was four or five, so IDK. Some were just plain old games and some were educational.
I am not a parent--I just stumbled upon this question, but IMO, I suggest you make sure to get him some nice, educational games now and as he gets older, just mix and match them. Also, my mom wouldn't let me play a lot of "M--Mature" rated game when I was ten/eleven/twelve, ect. so just try and make sure when he is older not to get him stuff like Grand Theft Auto.
Some game rated "T" for teen and "M" for mature differ in content. Like Wolfenstein 3-D is an older game, rated M, but its not that bad. Grand Theft Auto, also rated M, is just filled with adult content. Some T rated games are good for teens, while others should really have had an "M" rating, so just keep an eye on the games you get him, 'cause he'll probably want to keep playing games as he gets older.