Significance Left-handedness occurs in roughly 10% of people, but whether it involves altered brain anatomy has remained unclear. We measured left to right asymmetry of the cerebral cortex in 28,802 right-handers and 3,062 left-handers. There were small average differences between the two handedness groups in brain regions important for hand control, language, vision, and working memory. Genetic influences on handedness were associated with some of these brain asymmetries, especially of language-related regions. This suggests links between handedness and language during human development and evolution. One implicated gene is NME7 , which also affects placement of the visceral organs (heart, liver, etc.) on the left to right body axis—a possible connection between brain and body asymmetries in embryonic development.