if she dumps you because 'you play chess', there has to be another reason why she did it. you know, the real reason.
chess woes
It depends: if you played chess more than payed attention to her, then it's hardly surprising that she left you. If on the other hand she simply left you because you "play chess", then it strikes me that your ex-girlfriend is a shallow person and it's probably for the best that you don't try to get her back. Instead you should move on with your life and find someone better suited for you.
Just a thought, but could OP really mean, "How can I get her back for leaving me because I play chess?", as in, how can I get revenge?
If so I have few ideas; most of them are outlawed in many countries, but still...
If that is the only reason - which I doubt - then you should as well move on. If she won't respect your interest there is nothing you can't do. You can't pretend to be someone else just to please her tastes. Unless you neglected your relationship in favor of playing chess, then that would be your fault and the breaking up a consequence of your carelessness. That can't be helped unless you recognize where your priorities are.
Drop chess and take salsa-classes instead. If that still doesn't impress her, you'll have met at least new people who smell better than your chess companion... :-)

my girlfriend left me because i play chess. how can i get her back?