According to ChromeStory, the latest developer-focused Chrome OS version, Canary, has a flag you can use to toggle the feature:
"Instant Tethering Chrome OS
Enables Instant Tethering. Instant Tethering allows your nearby Google phone to share its Internet connection with this device. #enable-tether"
If you're running this early-adopter build of Chrome OS, you can enable this feature by typing chrome://flags into your URL bar, reports 9to5Google. You can enable the tether option there, restart the machine and then find Instant Tethering in the quick settings menu in the "network" section. The feature will also need to be toggled on your smartphone, which will also need to be a Pixel or Nexus device. With those caveats in place, however, you should be able to quickly tether up your Chromebook and easily get online without Wi-Fi.