I've got a Samsung Chromebook 303C which I find is pretty good for writing. Since I'm comfortable using a command line, I installed Ubuntu on it using a system called Crouton. This runs the Chrome and Ubuntu desktops simultaneously, so you can switch between them with a few key presses. You can install almost any Linux software on the Ubuntu side, including traditional offline apps. I'm a fan of minimalist word processors, so I chose one called FocusWriter.
One limitation of this particular Chromebook model is that it has an ARM CPU instead of the usual Intel type, so it can only run software that can be compiled for ARM. This excludes most non-open-source software, notably Dropbox, which I would have found useful. But I can always email my writing to myself for backup purposes, or use a USB drive. Crouton sets up Ubuntu so that it uses the same Download folder as the Chrome desktop, which gives an easy way to transfer files between them.
Aside from the lack of Dropbox, I think the ARM chip gives a very nice combination of cheap + light + good battery life (I regularly get 7 hours or more). It's not very powerful, but I don't need a powerful machine for writing. It is extremely quiet, and the keyboard and trackpad are much better than on my old netbook. All in all I'm very happy with it.