Feel free to inspect the background page and look at the network requests we're making. We're doing requests to Google Analytics to store counts (e.g. how many installs we have, how many notifications are clicked, etc.) but there is absolutely no data from the notifications or any personally identifying information about you.

It's not open source. You can verify this by the fact you have no login for Chime, so if you switch computers there's no "user profile" for you following you around. Beyond that, I'm not sure how else you want to verify this claim.