You may know that many Chromebook now can use Android apps from the playstore as well as apps from the Chrome webstore. I have been using Aquamail for 2-3 weeks now on my Chromebook and while it does have some quirks I've been getting by pretty well. One of the quirks is spell checks. Chrome OS and Android both have spell check but when I use my Chromebook in laptop mode with the physical keyboard while composing e-mail the Chrome OS spell check doesn't work and because I'm not using the virtual keyboard the Android spellcheck doesn't work. I have found no work around for this. Even the flipdog spellcheck doesn't work.
Supposedly Google is reaching out to app developers asking them to make their apps compatible with Chromebooks so this is one of things that needs to be addressed by someone.
