How can I protect Chrome user interface?

Google Chrome has a feature to change between Google accounts which allows several users to have their customized extensions, history and whatnot retrieved instantly. It doesn't, however, protect someone else from checking anything google related. That means anyone with access to your computer can check every google account that was setup as user in Chrome.

How can I prevent that? I first thought of checking a box with the option to have Chrome request for password upon user change but that doesn't seem to exist.

You cannot. The multiple profile support in Chrome is only for convenience and was never intended to be used as a security feature.

You will have to create separate user accounts in your OS to achieve any sort of security. In Windows, use Control Panel → User Accounts; in Mac OS X, Apple menu > System Preferences → Accounts.

Manage multiple users on Chrome

The ability to add multiple users to Chrome is intended to provide a quick and simple way to set up personalized copies of Chrome for people who are already sharing Chrome on the same computer today. It isn’t intended to secure your data against other people using your computer. To truly protect your data from being seen by others, please use the built-in user accounts in your operating system of choice.