In this paper we analyze eight years of employment data of a regional grocery store chain in the U.S. The data include job titles, wage rates, and earnings for all employees. We examine initial job assignments, mobility between departments, and mobility into supervisory and management positions in the firm. We model the flows of individuals between different departments and jobs within the firm as a Markov process. The estimated transition probabilities imply that expected seniority is greater for women. We find a pattern of intrafirm mobility and initial job assignment that generally penalizes women, even after taking account of individuals' characteristics.