We develop a two-sided multidimensional matching model of the market for CEOs that allows for both pecuniary and non-pecuniary (amenity) compensation. The model is estimated by maximum likelihood estimation using matched CEO-firm data from Denmark. We show that CEOs have preferences for building legacy and gaining empowerment. The legacy mechanism explains why there is low mobility in the CEO market, even though firms demand general CEO skills. The empowerment mechanism explains why CEOs are willing to sacrifice significant pecuniary income to manage high equity firms. The overall conclusion is that job amenities matter in the market for CEOs.