Most people have left‐hemisphere dominance for various aspects of language processing, but only roughly 1% of the adult population has atypically reversed, rightward hemispheric language dominance (RHLD). The genetic‐developmental program that underlies leftward language laterality is unknown, as are the causes of atypical variation. We performed an exploratory whole‐genome‐sequencing study, with the hypothesis that strongly penetrant, rare genetic mutations might sometimes be involved in RHLD. This was by analogy with situs inversus of the visceral organs (left‐right mirror reversal of the heart, lungs and so on), which is sometimes due to monogenic mutations. The genomes of 33 subjects with RHLD were sequenced and analyzed with reference to large population‐genetic data sets, as well as 34 subjects (14 left‐handed) with typical language laterality. The sample was powered to detect rare, highly penetrant, monogenic effects if they would be present in at least 10 of the 33 RHLD cases and no controls, but no individual genes had mutations in more than five RHLD cases while being un‐mutated in controls. A hypothesis derived from invertebrate mechanisms of left‐right axis formation led to the detection of an increased mutation load, in RHLD subjects, within genes involved with the actin cytoskeleton. The latter finding offers a first, tentative insight into molecular genetic influences on hemispheric language dominance.