Hey there!
The answer is yes. I have a Google Chromebook and it works wonderfully. I have yet to find a single complications with using the Chromebook. In fact, I do believe the OS is recommended on the Penn Foster FAQ page.
I bought mine a bout a year and a half ago when I began the program, and as I said it has worked wonderfully.
I wish you the best of luck and I hope that you have a splendid day!