https://docs.01.org/clearlinux/latest/guides/clear/swupd-3rd-party.html
How to install Google chrome using 3rd-party swupd?
To install Google Chrome with 3rd-party you would have to create your own repository for now. Until someone uploads their private repositories you will have to follow the guide to create your own, I did get it working on my machine locally but there is still some trickery involved with correctly creating the 3rd-party bundle (for example you need to fix the symlink such that the binary actually gets exported and is available in PATH) and you have to manually create the .desktop file in order for it to show up.