For those teachers using Moodle with Chromebooks, there is now a Secure Exam Browser that will help prevent students from accessing other websites during quizzes and tests, like the Safe Exam Browser does on Windows computers.
To access the Moodle Secure Exam Browser on a Chromebook, simply have students logoff or restart the Chromebook, then on the Login page, in the Apps menu (bottom left of the screen) pick Moodle - Secure Exam Browser.