There seems to be something wrong with Chrome’s spell check these days. A lot of users are reporting that this feature is either missing or not functioning properly.
Before we go to the fix, open chrome://settings/languages and make sure that you have checked “Enable spell checking” If it is already enabled, go ahead and try this temporary fix.
A temporary fix from the Chrome team
Go to Google Chrome Menu > Settings. Under Privacy, uncheck Use a web service to help resolve spelling errors
This should fix the issue for now. If you are still having trouble, one option is to install Chrome Spell Checker Extension. This extension gives spell check plus some more features.
*User-defined shortcuts, color
*User dictionary support
*Chrome context menu support
*User-friendly spell edit interface
Try this and let me know if it worked.