The Alternative Greek Keyboard Layouts extension for ChromeOS will let you type polytonic Greek on your ChromeBook, but the documentation isn’t great. Here’s the shortcuts I’ve found for the “Greek Polytonic” layout:
:
smooth breathing"
rough breathing;
acute'
grave[
circumflex]
iota subscriptq
;Q
:
I haven’t yet found a key for middot (·, ano teleia), but I’d love to be wrong!