Young children show significant changes in their mental-state understanding as marked by their performance on false-belief tasks. This study provides evidence for activity in the prefrontal cortex associated with the development of this ability. Event-related brain potentials (ERPs) were recorded as adults (N = 24) and 4-, 5-, and 6-year-old children (N = 44) reasoned about reality and the beliefs of characters in animated vignettes. In adults, a late slow wave (LSW), with a left-frontal scalp distribution, was associated with reasoning about beliefs. This LSW was also observed for children who could correctly reason about the characters’ beliefs but not in children who failed false-belief questions. These findings have several implications, including support for the critical role of the prefrontal cortex for theory of mind development.