In the healthy human brain, the processing of language is strongly lateralised, usually to the left hemisphere, while the processing of complex non-linguistic sounds recruits brain regions bilaterally. Here we asked whether the anterior temporal lobes, strongly implicated in semantic processing, are critical to this special treatment of spoken words. Nine patients with semantic dementia (SD) and fourteen age-matched controls underwent magnetoencephalography and structural MRI. Voxel based morphometry demonstrated the stereotypical pattern of SD: severe grey matter loss restricted to the anterior temporal lobes, with the left side more affected. During magnetoencephalography, participants listened to word sets in which identity and meaning were ambiguous until word completion, for example PLAYED versus PLATE. Whereas left-hemispheric responses were similar across groups, patients demonstrated increased right hemisphere activity 174–294 msec after stimulus disambiguation. Source reconstructions confirmed recruitment of right-sided analogues of language regions in SD: atrophy of anterior temporal lobes was associated with increased activity in right temporal pole, middle temporal gyrus, inferior frontal gyrus and supramarginal gyrus. Overall, the results indicate that anterior temporal lobes are necessary for normal and efficient lateralised processing of word identity by the language network.