We conduct a field experiment in which highly-ranked chess players play the centipede game in a natural setting. This game represents one of the main paradoxes of backward induction. In the experiment two players alternately are faced with the decision of either taking an exponentially growing pile of money and ending the game, or letting the other player make the decision. The player who decides to stop the game takes the larger portion of the pile, and the other player gets the remaining amount. All standard equilibrium concepts dictate that the player who decides first must stop the game immediately. There is vast experimental evidence, however, that this rarely occurs. Contrary to this evidence our results show that 69% of chess players stop the game immediately. When we restrict attention to chess Grandmasters this percentage escalates to 100%. We also conduct standard laboratory experiments where college students and chess players play ten repetitions of the game. We find that chess players playing versus other chess players rapidly converge to the equilibrium outcome, whereas students playing versus other students systematically depart from it. However, when students play against chess players the occurrence of the backward induction outcome increases tenfold.