Hair spray (alcohol base--- aqua net is what we used to use) may work. this would be something to test on a very small area to be sure it does not harm it. Acetone will work but it may, and likely will, harm the board (???). You need something like these.... some sort of alcohol based solvent that does not harm it. Rubbing alcohol *may* work or it may not, and it probbaly won't harm the board. I assume you tried water, which if not, may or may not work. I suggest you start with the weakest thing first (water, then rubbing alcohol, etc) and save acetone and harsh stuff for the last resort.
Removing ink from vinyl chess board
I believe acetone will melt the board.
Its very possible depending on what the material actually is. It melts a lot of plasticish materials for sure. Other types are fine, it even comes in a plastic bottle. As I said, try it on a tiny area before dumping a bottle out and use it as a last resort.

Thanks for the tips everyone. I used a little bit of water and got it to be very faint. Enough so that I would rather not risk ruining it with something else :P
My board isn't exactly old, maybe 5 or 6 months? I'd like to keep it for a little longer before reserving it for use as an analysis board.
How do I remove ink (I believe it was a standard ball point pen) from my vinyl chess board? Obviously I'd like to do so without damaging it.