I’m a little late to the game on this, but wanted to respond. I have wanted to get Rstudio Server running within crouton and then hit the server directly from the browser while in Chrome OS without having to open up an X window. Benefit is being able to pull out source tabs to their own window and I just think RStudio Server looks nice in the browser!
So, since I have other things I should be working on today I of course found the time to figure it out. It works really well! Now viewing html or pdf or docx from within RStudio just open in another chrome tab and I can get full screen for source tabs.
I want to play around with a different set-up on my chroot but once I do that will pull together a blog post about it. In the meantime, I followed that standard RStudio Server install directions (https://www.rstudio.com/products/rstudio/download-server/) and then followed directions on running servers in a chroot (https://github.com/dnschneid/crouton/wiki/Running-servers-in-crouton). With that done and the chroot and rstudio-server started, localhost::8787 gets me access directly from chrome os!