The pair beat out 10 other finalists: bubbles, the board game Clue, Fisher-Price Little People, little green Army men, the Magic 8 Ball, My Little Pony, Nerf toys, the Pac-Man video game, Teenage Mutant Ninja Turtles and the scooter.
Online polls had Teenage Mutant Ninja Turtles and My Little Pony running strong, but in the end a national selection committee made up of 23 experts, including toy collectors, designers and psychologists, voted in the winners.
"The two inductees ... are fantastic examples of the two extremes in the world of play," said Christopher Bensch, vice president for collections at The Strong Museum, which houses the 15-year-old hall.
"One is so strategic. It's rule-driven. It's something that adults play and puzzle over," Bensch said, "and at the other extreme is a toy that's pure fun. It has no rules. No one wins or loses. You squeeze it. You float it. It's so silly, so fun."
Anyone can nominate a toy for the hall of fame, but to make it through the selection process and become a finalist a toy must have achieved icon status, survived through generations, foster learning, creativity or discovery and have profoundly changed play or toy design.
"If there is a game you can call classic, this is that game," said curator Nicolas Ricketts as he introduced chess during an induction ceremony that featured the unveiling of chess- and rubber duck-themed cartoons by syndicated cartoonist Leigh Rubin.
Chess can be traced back centuries to an ancient Indian war game, but evolved into the game it is today by 1475, Ricketts said.
"In 1779, Benjamin Franklin wrote that playing this game inspires habits of foresight, circumspection and caution, all important traits in human life," he said. "Scholars today still study the effect of this game's play on the childhood brain and development."
The rubber duck "has been a fixture in pop culture for decades," curator Patricia Hogan said.
Although rubber toys first appeared in the late 1880s, no one knows exactly who hatched the idea of the rubber duck, museum officials said.
They weren't always meant for the bath - the first ones didn't float - but Ernie on "Sesame Street" secured its place in the tub with his 1970 ode, "Rubber Duckie." The song made it to No. 16 on the Billboard Top 40 chart.
To date, 53 toys are in the National Toy Hall of Fame, including alphabet blocks, the jump rope, playing cards, Scrabble and the stick.