Slitaz is tiny, runs in RAM and tends to just work in my experience: well worth a try if you want to get up and running quickly - http://www.slitaz.org

That said, Arch is much easier to set up than it might appear and would be a perfect base if all you're going to run is Chrome. No need for a desktop environment/window manager, either:

    xinit /usr/bin/chromium $* -- :1