During the last trimester of human pregnancy, the cerebral cortex of foetuses becomes greatly and quickly gyrified, and post-mortem studies have demonstrated that hemispheres are already asymmetric at the level of Heschl gyrus, planum temporale and superior temporal sulcus (STS). Recently, magnetic resonance imaging (MRI) and dedicated post-processing tools enabled the quantitative study of brain development non-invasively in the preterm newborn. However, previous investigations were conducted either over the whole brain or in specific sulci. These approaches may consequently fail to highlight most cerebral sites, where anatomical landmarks are hard to delineate among individuals. In this cross-sectional study, we aimed to blindly and automatically map early asymmetries over the immature cortex. Voxel-based analyses of cortical and white matter masks were performed over a group of 25 newborns from 26 to 36 weeks of gestational age. Inter-individual variations associated with increasing age were first detected in large cerebral regions, with a prevalence of the right hemisphere in comparison with the left. Asymmetries were further highlighted in three specific cortical regions. Confirming previous studies, we observed deeper STS on the right side and larger posterior region of the sylvian fissure on the left side, close to planum temporale. For the first time, we also detected larger anterior region of the sylvian fissure on the left side, close to Broca's region. This study demonstrated that perisylvian regions are the only regions to be asymmetric from early on, suggesting their anatomical specificity for the emergence of functional lateralization in language processing prior to language exposure.