International research on educational inequality consistently reports the existence of ethnic differences in school achievement. The paper explores as a prior stage early cognitive differences between 3- to 4-year-old natives and immigrants in Germany and tests whether ethnic differences in cognitive outcomes can be essentially explained by the parents’ social background and the home environment of the children. It is assumed that children’s later educational success depends on their abilities at preschool age. The acquisition of these abilities is determined particularly by the family, the children’s home environment and through institutional care. The data of a German project “Preschool education and educational careers among migrant children” reveal the existence of inequality in cognitive scores between natives and Turkish children. These differences cannot be explained by controlling for the social background of the families, nor by the home environment. A main result of the analyses shows that both factors are important.