Google Chrome "Tabs Protection Password" extension will satisfy your needs. It requires to enter an initial e-mail/password and it protects all opened tabs and also prevents the creation of new ones by requiring for your password.
It also hides all opened tabs so they are not visible by their titles.
- That does not guarantee that an advanced user will not disable the extension through Google Chrome settings
- You have to also enable it for Incognito mode (through Chrome settings) in order to work for this mode as well.
Despite the title, by reading "each time a person clicks on the browser", I understand that you need it globally for all tabs.