Previous research has consistently demonstrated a positive relation between firm size and skill premium. We decompose this result by type of skilled worker using data from Chilean firms and find that returns in skill premium to size are an order of magnitude larger for owners and managers compared to other types of skilled workers. We interpret this to imply that firm structure is important for understanding the relationship between skill premium and firm size. We propose an original model of firm hierarchy which rationalizes our empirical finding. In our model, more productive firms maximize profits by choosing to employ more levels of management. These managers require a higher average skill level and command a higher average skill premium. Additionally, our model predicts that skill premium is increasing in the ratio of workers to managers, a fact we also observe in the Chilean data.