A new Chrome OS commit suggests that integration with Android Messages could be on its way to the platform. The wording of the commit suggests that it will be a feature flag, at least in the beginning, but there are no details on how to enable the flag or when it will appear in a Chrome OS build.
Integration with Android Messages would allow for users to have their SMS/MMS messages on their Android phone running Messages to be sync’d with their Chromebook, thus allowing you to respond from your Chromebook without having to actually pick up your phone. In theory, it works on the same principle as what you can do with Hangouts Classic before SMS support was removed (but it still works for Project Fi users) between your phone and your Chromebook.
Of course the bigger example of this cross device integration is Apple Messages where you can respond to a text message on your MacBook.
How this ultimately is developed and works on Chrome OS is not clear nor is it clear when we will see this in a Chrome OS build. No matter how you look at it, we are probably several months away from seeing this in a build. But the good news is that there is a Chrome OS commit to see this through and make it happen.