In Chrome, clicks and user activity is tracked locally just like any other browser.
What is sent back to google is your searches, or partial searches, for auto-complete suggestions, and if you have instant search on, pretty much everything you type in the Google search bar.
They also track your sync data (bookmarks, history, etc.) You can see exactly what Google says they track here: https://www.google.com/intl/en/chrome/browser/privacy/.
Some people speculate that Google also tracks a code string that is non-identifying, and used to measure the success of Google's Chrome promotion/marketing campaigns, along with early usage notes. However that last part is not officially acknowledged by Google.
Since Chromium is the open source browser it definitely does not track your user activity for marketing stuff. However it does track your click, if you mean by where you are surfing too, every browser does. If you want to stop this, go to settings and turn on "Do Not Track."