MuseScore's desktop program will not work natively on Chrome OS, but there are some workaround solutions:
Since Chrome OS 69, certain chromebook models are able to run Linux apps and so you can install MuseScore for Linux as provided on our Download page. Feedback about the installation process and supported hardware is welcome on the forum
Via software-on-demand service such as rollApp: By just visiting this website, you can run MuseScore in the browser. You can access your scores via cloud services such as Google Drive or save them to your online MuseScore account through the menu File→Save Online.... Note that currently, sound and playback does not work on rollApp.
Via Crouton: Involves installing a Linux based operating system which runs in parallel with Chrome OS, and then installing MuseScore on Linux.
Alternatively, it is possible to install MuseScore's Android app on recent Chromebooks. You will need to update to the latest version of Chrome OS first. See the Chromebook support documentation for help installing Android apps on Chromebooks, and a list of supported devices. The app only supports playback of existing scores, not score editing or creation, but you can sign-in to your MuseScore account for easy access to all your scores on MuseScore.com.