Ethnicity wage gaps in Great Britain are large and have persisted over time. Previous studies of these gaps have been almost exclusively confined to analyses of household data, so they could not account for the role played by individual employers, despite growing evidence of their wage-setting power. We study ethnicity wage gaps using high quality employer-employee payroll data on jobs, hours, and earnings, linked with the personal and family characteristics of workers from the national census for England and Wales. We show that firm-specific wage effects account for sizeable parts of the estimated differences between the wages of white and ethnic minority workers at the mean and other points in the wage distribution, which would otherwise mostly have been attributed to differences in individual worker attributes, such as education levels, occupations, and locations. Nevertheless, there are substantial gaps between the wage structures of white and ethnic minority employees which cannot be accounted for by who people work for or other attributes, especially among higher earners.