not completely, but fairly close.. there are still some limitations in how it works that someone with enough intention could pin it down. (by controlling edges, using traffic analysis, etc.. it is hard to do, but there are at least theoretical attacks).
if your using chome... your already sending all your data to google
even if you use it over chrome, there is user behavior that could be used to track you from site to site/etc. yes, you are going to be generally more secure using tor then chrome, but don't assume perfect anonymity.