When Michelle Kong started a chess club last year, hoping to meet other players in their 20s, attendance was so meager that she needed only one chessboard. She posted about the club on social media until a tattooed cross section of young people in Los Angeles began showing up to exchange pawns and phone numbers.

Before long, boxes of triple-weighted bishops and rooks were piling up in the back seat of Ms. Kong’s sedan. Last December she upgraded the club’s home base from a cozy jazz bar to a warehouse that was barely large enough to accommodate the 500 people who attended the Thursday night meetings of the group, LA Chess Club, this summer.