ClipChamp - a Chrome extension & a Chrome app
Clipchamp’s main purpose is to convert and compress video files, which is useful if you have videos that you want to watch on your Chromebook but that don’t play due to an unrecognised video codec.
However, the app also comes with an extra feature that allows you to record short videos with your webcam that you can save locally, on Google Drive or share directly on Facebook or YouTube.
Screencastify - a Chrome extension
Records video (selfie mode?) with audio from a Chromebook. Can also record audio while showing what's on your screen (explaining a web site or Google Doc, for example). https://www.useloom.com/
School Video Recorder for Google Drive
NOT free - but you can do up to ten free assignments for up to 20 students: