Are women innately inferior to men at playing chess?

No:

Women are surprisingly underrepresented in the chess world, representing less that 5% of registered tournament players worldwide and only 1% of the world’s grand masters. In this paper it is argued that gender stereotypes are mainly responsible for the underperformance of women in chess. Forty-two male-female pairs, matched for ability, played two chess games via Internet. When players were unaware of the sex of opponent (control condition), females played approximately as well as males. When the gender stereotype was activated (experimental condition), women showed a drastic performance drop, but only when they were aware that they were playing against a male opponent. When they (falsely) believed to be playing against a woman, they performed as well as their male opponents. In addition, our findings suggest that women show lower chess-specific self-esteem and a weaker promotion focus, which are predictive of poorer chess performance.

Source: “Checkmate? The role of gender stereotypes in the ultimate intellectual sport” from European Journal of Social Psychology, Volume 38 Issue 2, Pages 231 – 245