I dont have any knowledge in this area but i dont think this has
anything to do with chrome, i think it's an intel graphics driver
issue, it does not handle gracefully when the video memory is gone.
Well, you state in your original email that you have no swap partition. Which is like tying one arm of the kernel behind its back. When the memory is full, what do you *expect* to happen. Something needs to get killed, and the X server does use a lot of memory so it is a good choice.
You could disable memory overcommit, that would cause things to fall over sooner.
You could change the OOM priority of the X server, this would cause some other process to be killed instead.
Or (recommended) just add a small swap partition (say 128MB) to allow the kernel to put unused memory pages on disk so the X server can use them instead.