Since version 47, Chrome supports multi-lingual spell-checking. I didn't find too much information about it, only this post because I came across an issue with it (I had to remove and add "Spanish" again to make it work).
With Chrome Version 47, there is a new schema for multilingual
Spell-Checking. Chrome now automatically detects what language(s) you
are using. To specify which languages you want to check, please do
this: Click the Menu Icon (≡), then Settings -> Advanced Settings,
then scroll down to Languages. Now click the Button [Settings] to set
the languages you want to use for spelling.
NOTE: And for those who also use Firefox besides using Chrome, a new equivalent extension has been released: automatic-dictionary-switcher