Japanese atomic bomb survivors irradiated 8-25 weeks after ovulation subsequently suffered reduced IQ [Otake and Schull, 1998]. Whether these findings generalize to low doses (less than 10 mGy) has not been established. This paper exploits the natural experiment generated by the Chernobyl nuclear accident in April 1986, which caused a spike in radiation levels in Sweden. In a comprehensive data set of 562,637 Swedes born 1983-1988, we find that the cohort in utero during the Chernobyl accident had worse school outcomes than adjacent birth cohorts, and this deterioration was largest for those exposed approximately 8-25 weeks post conception. Moreover, we find larger damage among students born in regions that received more fallout: students from the eight most affected municipalities were 3.6 percentage points less likely to qualify to high school as a result of the fallout. Our findings suggest that fetal exposure to ionizing radiation damages cognitive ability at radiation levels previously considered safe.