Using detailed administrative data for public schools, we document racial and ethnic segregation at the classroom level in North Carolina, a state that has experienced a sharp increase in Hispanic enrollment. We decompose classroom-level segregation in counties into within-school and between-school components. We find that the within-school component accounted for a sizable share of total segregation in middle schools and high schools. Recognizing its importance could temper the praise for school assignment policies that reduce racial disparities between schools but allow large disparities within them. More generally, we observe between the two components a complementary relationship, with one component tending to be large when the other one is small. Comparing the degree of segregation for the state's two largest racial/ethnic minority groups, we find that White/Hispanic segregation was more severe than White/Black segregation, particularly within schools. Analyzed as separate administrative units, schools with large shares of Black students tended to have more White/Black segregation across classrooms than schools with smaller shares. Finally, we examine enrollment patterns by course and show that school segregation brings with it differences by race and ethnicity in the courses that students take, with White students more likely to be enrolled in advanced classes.