He’s the fastest climber alive. He trains by playing chess.

That’s when Watson, an 18-year-old from Texas, leans over a chess board and focuses on the one skill that unites nerdy grandmasters and turbocharged athletes who fly up 49-foot walls in less than 5 seconds.

Watson’s gravity-defying secret isn’t strapping himself to a jetpack. It’s training his mind through three-minute games of blitz chess to identify patterns and make split-second decisions. That, he says, is what will determine whether he’s an Olympic speed-climbing champion—or just another guy who falls off the wall with chalk on his hands.

“When you’re playing blitz, you’re really moving off intuition," Watson says. “You’re thinking about it, but you’re also thinking about your time: How can I make the best move—or close to the best move—without making a mistake?"

Whenever Watson stands in front of a wall, it takes him almost no time to spot the winning line. At the Climbing World Cup in April, his time of 4.798 seconds set a new world record. The previous mark, 4.859 seconds, was also Watson’s—he’d set it earlier that same day. Watson will take another shot at the record this week when he competes on the Olympic wall just outside Paris.

In the meantime, he is spending whatever spare moments he has in the dining hall at the Athletes’ Village with a chessboard and a sign, inviting any and all challengers in seven languages. His opponents might be playing for fun. What they don’t realize is that they’re helping Watson train for gold.

“Chess is definitely a game about decision-making," says American grandmaster Hikaru Nakamura, widely recognized as one of the greatest speed chess players ever. “And any sport that requires on-the-fly decision-making, it can help a lot."

Watson grew up in Southlake, Texas, a place better known for producing five-star football recruits than five-second climbers. But as a child, he had a habit of clambering up the shelves of his family’s pantry. His parents thought it was the cutest thing. They also thought it was completely terrifying.

The only logical solution was to teach him how to climb safely and to reach for something other than the cookie jar.

By the time he was in his mid-teens, Watson’s gift for hauling himself up anything that pointed skyward had already landed him on the global stage. He won his first World Cup at 16 years old and knew that his next summit could only be Olympic gold.

When it was time to take his game to the next level, though, climbing coach Albert Ok had little interest in judging Watson on how quickly he could reach the top of a vertical wall. Instead, he prefers to evaluate his students on how they push pawns around a horizontal board. If they can handle defeat against him, he knows they’ll be able to stand up to the rigors of climbing.

That’s not to say Watson enjoyed it when Ok crushed him the first time they played—especially since Ok beat him while wearing a blindfold. But it was enough to get Watson hooked.

That made him one of a growing number of high-performance athletes who include chess in their mix of training tools. NFL quarterbacks such as the Cincinnati Bengals’ Joe Burrow play to improve their mental processing. Spanish tennis prodigy Carlos Alcaraz likes to squeeze in a quick game before matches to focus his mind. And Dallas Mavericks’ star Luka Doncic plays constantly on his phone.

Watson is the rare athlete who plays a sport that’s actually faster than blitz chess. To him, a three-minute clock might as well be a one-week calendar. In one of Watson’s favorite drills, he races an opponent up the wall. Then they battle over the board. They keep alternating, with each climb and chess game counting for one point, until someone gets to seven.

Watson believes that it not only sharpens his ability to see moves into the future. It also simulates the relentless pressure of high-level competition.

“You’re constantly working for about 45 minutes," Watson says. “That’s the same thing as a speed final would be at the Olympics."

His coach is fully on board and likes to put things in terms Watson can understand. As they break down strategy on the wall, Ok talks about positions and endgames. And when he lays out his ambitions for Watson, he doesn’t compare him to any other climber.

Instead, Ok reaches for the Norwegian chess legend Magnus Carlsen: “I’m trying to make you the Magnus of speed climbing."

Write to Andrew Beaton at andrew.beaton@wsj.com and Joshua Robinson at Joshua.Robinson@wsj.com