How protect chrome extension

The premise seems to be simple. By default browser interprets HTML/Javascript, so are the chrome extensions which run along with the page.

One way is to obfuscate your javascript code , or rely on NPAPI compiled-binary plugins, or use NaCL

Obfuscating the code might no longer be a solution after Chrome forbade obfuscating extensions: https://stackoverflow.com/a/49509913

In case you have some proprietary code (e.g. special algo you want to keep safe etc') and you are targeting Chrome - I would suggest to go with Native Client. Nacl let you run C/C++ code in your browser. It's very powerful and you can be sure it will be very hard for someone to pick into your binary.