How do I hide my API Key in Chrome Extension?

I am going to be using youtube API and will need to use a key, but publishing the key would just give it access to all users. How can I hide it? After doing some research I learned that I can create a web server and use that to capture the key? I am new to web server and know little about them? How can I go about creating such server that provides me with a key on request and will the user be able to also call that request if they look around the code?