We investigate the glass ceiling hypothesis according to which there exist larger gender wage gaps at the upper tail of the wage distribution. We demonstrate that in some circumstances, more qualified women may be offered lower wages than men at the equilibrium. This occurs for instance in a competitive model of wage determination where employers face gender-specific probabilities concerning the stability of their employees in their firms. Then, we focus on the relevance and the magnitude of the glass ceiling effect in France using a matched worker-firm data set. We estimate quantile regressions and use a principal component analysis to summarize information specific to the firms. Our different results shows that accounting for firm-related characteristics reduces the gender earnings gap at the top of the distribution, but the latter still remains much higher at the top than at the bottom.