Yes! It's possibly to do coding on Chrome OS, especially web applications like you mention!
For light projects, you could probably get away with a good text editor and SSH client. The best text editor I've found so far is Caret. SFTP and other file systems can be added too which really helps. Of course, this is assuming you have a server somewhere to actually run things.
If you don't have a server, definitely consider the hosted IDEs others mentioned. They're nice because you can focus more on your app and less on server maintenance.
But for something not requiring internet access, I'd suggest installing Ubuntu or Debian with Crouton. It's easy to do, and you could get away with just installing the CLI components. That way you can run npm, gulp, wiredep, bower, yeoman, etc.
And this is why I stick with Caret.
...or did, until I mostly decoupled myself from the Google ecosystem (and they stopped supporting Chrome apps off of ChromeOS). Still, if somebody, I dunno, put it together to run off of Electron or something, I'd definitely go back to using it instead of Sublime.
Side note: finish porting caret to electron