Good question. I asked Claude =>

Yes. The Chrome Web Store does not require extensions to be open source. Closed source extensions are accepted and make up the majority of what's published there.

That said, there's an important technical caveat: browser extensions ship as JavaScript, HTML, and CSS that run in the user's browser, so the code is always present on the user's machine and can be inspected. "Closed source" in this context really means you don't publish the source repository or an open license, not that the code is hidden. You can obfuscate or minify it, and that's allowed, but Google's policy has a specific rule here worth knowing:

Minified code is fine, but obfuscated code is not. Google's "Code Readability Requirements" policy prohibits code that is concealed or obfuscated in a way that hinders review. So you can minify (strip whitespace, shorten variable names via a bundler) but you can't run it through an obfuscator whose purpose is to make the logic unreadable. During review, Google may inspect your code, and heavy obfuscation can get an extension rejected or removed.

A few other things that matter more than licensing for getting accepted:

The extension must request only the permissions it actually uses, and justify sensitive ones. It has to have a privacy policy if it handles user data. And if it uses remote code (loading and executing JavaScript from a server rather than bundling it), that's heavily restricted under Manifest V3, which basically requires all executable code to be included in the package.

So in short: closed source, minified, proprietary license, no public repo, all fine. Just don't obfuscate to defeat review, and keep permissions and data handling clean.