There are sizable and pervasive academic achievement gaps between minority and non-minority students in the United States. Non-minority students -- particularly boys -- are more likely to enroll in school one year after they become eligible, a practice known as 'redshirting.' Consequently, non-minority students are on average more mature than minority students when they take standardized tests. Many studies have documented that differences in maturity at the moment of testing translate into large differences in test scores. Thus, differences in redshirting behavior across minority and non-minority students may be a contributing factor to achievement gaps. This study analyzes the effect of redshirting on achievement gaps using a reform in North Carolina that shifted the cutoff date for school eligibility in 2009 from October 16 to August 31. We use the reform to create an instrumental variable for redshirting behavior. Using data for eight cohorts of 3rd graders in the Wake County Public School System and a difference-in-differences approach, we estimate that redshirting increases the achievement gap by 28%--30% among boys born close to the cutoff date for school eligibility, and 3%--4% among all boys. For girls, the estimates are 8%--11% for those born close to the cutoff and 1% overall, but these estimates lack statistical significance. We discuss some policy implications of shifting the cutoff date for school eligibility -- 14 states have done since 2000 -- and growing redshirting rates.