The obvious first change would be to switch out the default browser - Firefox OS? Opera OS? This would depend on putting the X stack back into Chrome OS, since if I recall correctly Google dropped that. It's definitely possible, though. I think the harder part would be making the necessary modifications to the browser to allow it to be used as the sole interface to the system. Chrome can apparently view folders, and supports pinning web apps to a menu; I don't know if other browsers would want to do things exactly the same way, but they'd have to do something similar.
We could also switch in other non-browser applications. The command-line addict in me would love to have an OS that boots straight to a command line, and can connect to the internet so I can ssh. Having that on a netbook that I can carry around would be insanely useful. Application vendors could also create single-application systems as demos (and if they do, people will be trying out their apps running on Linux!).
Some people are going to ask what the point is. We already have much more capable Linux distros that can do the same thing, so what's the point? The interesting thing that Chrome OS adds is completely safe, transparent upgrades, and a read-only root. This has two humongous implications for the end-user: they don't have to worry about software upgrades ever, because the system auto-updates, and they can always reboot the system to get it back to a known-good state. Yes, this also means that you lose a lot of flexibility with the system; it's a tradeoff, and in many cases, the benefits of this outweigh the costs.
The core interesting idea of Chrome OS that we can use is the idea of "appliance computing". Looking at it a certain way, the OS really doesn't matter at all - what the user cares about is the application. Chrome OS, minus Chrome, gives us the necessary foundation to build completely stripped-down single-application systems. Obviously, this isn't going to be useful for everybody in all cases, but it's a pretty interesting idea to play around with.
I think the first step should be factoring out the "OS" part of Chrome OS. It'd be useful to have a core OS part, which automatically updates in the background, and an application part, as an image which is overlaid on the OS and contains the application. This way, there could be a single shared source for OS upgrades for all the different single-app systems. It would also make it pretty easy to make your own computing appliance, since you'd just have to package up the necessary files. There would need to be a dependency system so that version mismatches between the two parts don't cause problems, but this is a problem that Linux distros have explored pretty thoroughly.
This is kind of drifting into some ideas I've had about new ways that distros could be structured, but that's a whole other topic for a whole other post. ;)