No it doesn't: https://www.google.com/intl/en-US/chrome/browser/privacy/
Your search history is used (if you have it turned on), but that's just from using google.com for search and is independent of the browser you use.
The means may be different, but the ends are the same: users are tracked all across the Internet.
It's a bit confusing for me, it looks like they are collecting visited urls as they are not considered personal identifying information.
I've just learned that with the spellcheck feature they are basically receiving all the text I write on the Internet to their servers.
By the way are we really discussing about the privacy policy of a company that sent its data to NSA? I'm not condemning them, still we should be aware of this and never forget.