Here are two ways to take screenshots using a Chrome browser: Capture, Explain and Send Screenshots, and Numbus.
Nimbus seems a little more robust than Capture, Explain … I just came across it and updated this post. You can do more with it including create a screencast. I’d go with this one, but I’ll leave them both here for you to decide. Both will do the job.
Here is a brief video about how to use a Chrome extension called Capture, Explain and Send Screenshots. It is easy to download the completed images to Google Drive.
If you are looking for a way to take and annotate screenshots on a Chromebook, this might be something to look at.