The term "cerebral torque" refers to opposing right-left asymmetries of frontal and parieto-occipital regions. These are assumed to derive from a lateralized gradient of embryological development of the human brain. To establish the timing of its evolution, we computed and compared the torque, in terms of three principal features, namely petalia, shift, and bending of the inter-hemispheric fissure as well as the inter-hemispheric asymmetry of brain length, height and width for in vivo Magnetic Resonance Imaging (MRI) scans of 91 human and 78 chimpanzee brains. We found that the cerebral torque is specific to the human brain and that its magnitude is independent of brain size and that it comprises features that are inter-related. These findings are consistent with the concept that a "punctuational" genetic change of relatively large effect introduced lateralization in the hominid lineage. The existence of the cerebral torque remains an unsolved mystery and the present study provides further support for this most prominent structural brain asymmetry being specific to the human brain. Establishing the genetic origins of the torque may, therefore, have relevance for a better understanding on human evolution, the organisation of the human brain, and, perhaps, also aspects of the neural basis of language.