I think a number of stories could fit that description. Elizabeth playing chess with Darcy is a favorite piece of fanfic lore, almost up there with Darcy having big hands that engulf Elizabeth's small, delicate ones.
There is a story not on this site which features that bit rather prominently. They play at Netherfield. It's on an adult site so I cannot mention the name here. That story is also set apart by the sparkling banter between Darcy and Elizabeth. Some of the best writing you will find, which is a high compliment given the fine writing available in JA fanfic. This particular story is unfortunately incomplete -- for several years now.
