The formation of human capital is important for a society's welfare and economic success. Recent literature shows that child health can provide an important explanation for disparities in children's human capital development across different socio-economic groups. While this literature focuses on cognitive skills as determinants of human capital, it neglects non-cognitive skills. We analyze data from economic experiments with preschoolers and their mothers to investigate whether child health can explain developmental gaps in children's non-cognitive skills. Our measure for children's non-cognitive skills is their willingness to compete with others. Our findings suggest that health problems are negatively related to children's willingness to compete and that the effect of health on competitiveness differs with socio-economic background. Health has a strongly negative effect in our sub-sample with low socioeconomic background, whereas there is no effect in our sub-sample with high socio-economic background.