Is there an extension that does this? I have successfully created another user but would also like to password protect it.
The official stance:
Can I protect the user I created with a password, so other people can’t access it?
Chrome does not provide password protection for this feature. Adding new users to Chrome isn’t intended to secure your data against other people using your computer. Chrome provides this functionality as a quick and simple user interface convenience for people who are already sharing Chrome on the same computer today. To truly protect your data from being seen by others, please use the built-in user accounts on your operating system of choice.