The complexity of neural activity is a commonly used readout of healthy functioning in cortical circuits. Previous work has linked neural complexity to the level of maternal care in preterm infants at risk for developing mental disorders, yet the evolution of neural complexity in early human development is largely unknown. We hypothesized that cortical dynamics would evolve to optimize information processing as birth approaches, thereby increasing the complexity of cortical activity. To test this hypothesis, we conducted a cohort study relating prenatal neural complexity to maturation. Magnetoencephalography (MEG) recordings were obtained from a sample of fetuses and newborns, including longitudinal data before and after birth. Using cortical responses to auditory irregularities, we computed several entropy measures that reflect the complexity of the MEG signal. Despite our hypothesis, neural complexity decreased significantly with maturation in both fetuses and newborns. Furthermore, we found that complexity decreased significantly faster in male fetuses for most entropy measures. Our surprising results chart the evolution of neural complexity in perinatal human development and may lay a foundation for future work that would relate fetal neural complexity to developmental phenotypes, especially in the area of perinatal risk where biomarkers are greatly needed.