I've seen several questions from other users asking how to access their Dropbox files in Chromebook devices.
In all cases the only option is a third-party app on the Chrome Store. On the basis of that app's reviews, I am not inclined to use it. It's unreliable and does not behave itself well in the context of Chrome OS.
Surely this is something the good people at Dropbox should, themselves, provide. Is there anything in the pipeline?