In Chrome, every time you start to type a URL, it tries to autocomplete. One source of autocompletions is that it contacts Google, which sends back suggestions. Therefore by default Google knows every search you do in Chrome, even if you didn't want to go to Google. (They turn this off for incognito mode.)
I don't know how long this has been the case for Chrome, but I use this feature a lot more than I'd use Canonical's search.