Most people have a right-ear advantage for the perception of spoken syllables, consistent with left hemisphere dominance for speech processing. However, there is considerable variation, with some people showing left-ear advantage. The extent to which this variation is reflected in brain structure remains unclear. We tested for relations between hemispheric asymmetries of auditory processing and of grey matter in 281 adults, using dichotic listening and voxel-based morphometry. This was the largest study of this issue to date. Per-voxel asymmetry indexes were derived for each participant following registration of brain magnetic resonance images to a template that was symmetrized. The asymmetry index derived from dichotic listening was related to grey matter asymmetry in clusters of voxels corresponding to the amygdala and cerebellum lobule VI. There was also a smaller, non-significant cluster in the posterior superior temporal gyrus, a region of auditory cortex. These findings contribute to the mapping of asymmetrical structure–function links in the human brain and suggest that subcortical structures should be investigated in relation to hemispheric dominance for speech processing, in addition to auditory cortex.