That could be said about any browser. They all store your browsing history somewhere on the machine. You can usually clear your browsing history in all the browsers in the preferences, including Google Chrome. If I want to be really paranoid just go into the system files and look for and delete the profile folder, you will of course delete all your bookmarks, but they should be backed up somewhere anyway.
Best Android apps 2015/2016: Best apps for your new phone or tablet - what apps should I download?