As I recall, the deal was something like: the chess-club guy tipped off the chemist about the victim's chess strategy (sorry, it's been a while and I don't remember the names), and the victim was about to denounce him for this betrayal, so he felt that he had to kill her.
What I don't understand is the nature of the supposedly-secret information that the murderer had given to the chemist in order for the chemist to beat the victim. As I understand it, in a chess club (much less a tournament), matches are not only open but recorded and discussed in detail, along with "You could have done this..." If the murderer had some insight into the victim's chess strategy, I would hardly have thought that it would be some sort of secret.
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