A few months ago I happened upon the MediaCore Capture Chrome Extension while doing some research for a secondary English teacher.
This awesome extension is chromebook friendly and VERY easy to use. You have 2 options for recording: Desktop and Webcam. With the desktop option, you can also choose to embed the webcam - great for flipped classroom videos!
When you have finished recording, you will be redirected to the Review tab where you can upload your recording to a MediaCore site (requires an account) or download it (will save in file box on Chromebook).