oubless is correct. Most browsers do not allow you to access different domains using XHR for security purposes. Even if you could, I'm fairly certain that the folks at Google wouldn't be very happy about what you're trying to do. If you are interested in having a Google search on your website check
this link out.
Also, you should consider using
prototype.js which I personally highly recommend or another JavaScript library. Prototype and many other libraries provide a much more programmer friendly interface for crating AJAX requests...its much easier and cleaner than using XHR yourself.
Happy Coding.
-Fahlyn