Every modern browser tracks you - ever since the inception of the browser cookie in Netscape 0.9. Google has been clear and upfront about their data useage - and you can OPT OUT. You have privacy settings that allow you to block Google's ability to track you, or any other third party through the browser itself. Laws passed in 2011 make such tracking without consent and/or not having the ability to disable it illegal. This, of course, does not stop outside tracking, such as what may be used by your ISP or your workplace (or malware), but that's outside of the browser developer's control.
So, no, there is nothing wrong with them using Chrome. Or IE. Or Firefox. Or Safari. etc. I'd be more worried about a home-brewed browser that may not follow privacy regulations like Chrome does.