Source: 9to5GoogleGoogle Stadia is the next Google service to getting messaging baked in, which is an essential feature for a lot of gamers. Messaging is coming to every country Stadia supports—US, Germany, Canada, Finland, Denmark, France, Sweden, Netherlands, Norway, Belgium, Ireland, the UK, and Spain.
It's expected to appear on the web app the next time you load it home. 9to5Google says you might need force stop the app on Android to get it. They didn't mention when iOS will get the feature as well.