Early cortical folding and the emergence of structural brain asymmetries have been previously analyzed by neuropathology as well as qualitative analysis of magnetic resonance imaging (MRI) of fetuses and preterm neonates. In this study, we present a dedicated image analysis framework and its application for the detection of folding patterns during the critical period for the formation of many primary sulci (20-28 gestational weeks). Using structural information from in utero MRI, we perform morphometric analysis of cortical plate surface development and modeling of early folding in the normal fetal brain. First, we identify regions of the fetal brain surface that undergo significant folding changes during this developmental period and provide precise temporal staging of these changes for each region of interest. Then, we highlight the emergence of interhemispheric structural asymmetries that may be related to future functional specialization of cortical areas. Our findings complement previous descriptions of early sulcogenesis based on neuropathology and qualitative evaluation of 2D in utero MRI by accurate spatial and temporal mapping of the emergence of individual sulci as well as structural brain asymmetries. The study provides the missing starting point for their developmental trajectories and extends our understanding of normal cortical folding.