Quilgo lets you put a timer on a Google Form as well as limit the time the form is available to be completed, for FREE. You can have up to 100 tests under the free account.

A paid account throws in the ability to access and monitor the testers web cam to verify who is staking the test and can also screen record the tester to ensure test security.

Best of all I tested this and it actually works. When the timer ran out on my “test” it closed out on me. Keep in mind that does mean if it is not completed and submitted with in the allotted time the work will be lost. If web camera is enabled it won’t let the tester access the test without a webcam, which school chromebooks do have.