A short story written by Roger Zelazny (1982) (and providing the title for a collection of his stories, Unicorn Variations).

First, a synopsis

A washed up chess player, out doing some hiking, rests in an Old West ghost town, and fiddles with a dusty chess set, reliving his past glory. When he's had enough, he resets the pieces, only to find that the King's pawn has been advanced to K4. Taking this in stride, he plays his invisible opponent, whom he discovers to be both an accomplished chess player and a fan of beer.

Later, the opponent exerts his will, allowing Martin to see his true self -- a unicorn unusual not only for being completely black, but (as he explains) his ability to travel to Earth from the "morning land" where mythical creatures live. He's here to reconnoiter, as the way will soon be opened for unicorns to live on the Earth. Martin's questions bring forth Tlingel's explanation that every time a natural species becomes extinct on Earth, a mythical species is able to take up residence here. For example, the Loch Ness Monster slipped in when the dodo disappeared.

Humans being (in some respects) of a higher order, naturally their successors have to be pretty special themselves -- say, unicorns (which are known to be a bit arrogant). Tlingel is here to check out the situation, and maybe expedite things a bit with a nudge in a vulnerable spot.

Martin doesn't like the sound of that, and ends up challenging Tlingel to another chess game. If Tlingel loses, he agrees not to mess with the natural order here, and if he wins... well, of course he'll win, he's a unicorn. Martin gains a concession that at, any point during the game, he can take a month off to study the position, since so much is riding on the outcome. They play several moves, then Martin requests his first adjournment.

After fixing up the dilapidated saloon, he strikes out for the forest to spend the rest of the interlude in contemplation. Napping under a redwood tree, leaving the board set up with Tlingel's last move, he awakes to a large hairy creature mulling it over. "White's pawn should take the pawn" says Grend the sasquatch. The presence of a sasquatch is insignificant in Martin's mind compared to the (ludicrous, he thought) idea that BxN is not the best move. Grend offers to play either side, assuring Martin that he will win. Which he does. Martin congratulates him.

Yes, we bigfeet are pretty good, if I do say it. It's our one big recreation, and we're so damned primitive we don't have much in the way of boards and chessmen. Most of the time we just play it in our heads.

With the month expired, Martin is back in the saloon, and when Tlingel appears, plays Grend's move. He feels a bit guilty playing them off one against the other, but with mankind's survival at stake, he does so anyway. After several more adjournments and strategy sessions with Grend, Tlingel declares the game a draw. After which, Grend, some of his sasquatch friends, and Rael the griffin show up for more beer.

Author's notes

According to Zelazny, he wrote this story several months after he mentioned to George R. R. Martin that two anthologizers had approached him recently, one asking for a story about a unicorn, the other a story set in a barroom. He had neither. Martin mentioned that a third was preparing a collection of stories with a chess theme, and suggested that Zelazny should write a story involving a unicorn and chess, and have it take place in a bar. Then sit back while the money pours in from three different directions.

When he later decided to do so, he did some research and found an account of a tournament in 1901 in which two of the defeated contenders huddled with the one remaining player, Halprin, who was considerably weaker than the favorite, Pillsbury, the night before the title match and coached him on what to expect. Pillsbury fell behind initially, seeing a much better game come at him than he had expected, but fought back to a draw. In Unicorn Variation, their title game is replayed by Martin and Tlingel.