[RaitoBezarius]

You can ask the user to pay a subscription fee to use the extension. (a freemium model for example).

Then, the user, in fact, pays only for using the back-end API. The front-end, of course, is like a website, """open-source""".

[justanton]

does Chrome Web Store have this feature built-in (to offer and process payments for extensions)?

[erikrothoff]

And yes, Chrome web store allows payments. We have http://braintreepayments.com and http://paypal.com. Having them play together is hard enough...