While you can use the new Android Messages for web on any supported browser, it obviously works well on a Chromebook too. Setup is simple using a browser and the recently updated Android Messages app.
Messages
“Better Together” bringing instant tethering, SMS, and easy unlock to Chromebooks

Kevin C. TofelNews6 Comments on “Better Together” bringing instant tethering, SMS, and easy unlock to Chromebooks
All in all, Better Together seems more like a branded bundle and simple setup of currently existing features. That’s not a bad thing as many Chromebook users likely don’t know about or use features like Instant Tethering, SMS integration and Smart Lock.
Google rolls out Android Messages support for Chromebooks and web browsers

Kevin C. TofelNews4 Comments on Google rolls out Android Messages support for Chromebooks and web browsers
This doesn’t quite look like the “Better Together” service I reported on earlier in the month, however, Google announced Android Messages support for the web today. The feature will allow Chromebook users and those on desktops to send, receive, and reply to messages directly in the browser.
Chromebooks getting native Android Messages support called “Better Together”

Kevin C. TofelNews3 Comments on Chromebooks getting native Android Messages support called “Better Together”
Hot on the heels of news indicating that Chromebooks will eventually support Project Fi and eSIM capability, Google is looking to bring Android Messages support to Chrome OS devices.