Firms are born small, grow, and die. We investigate an explanation for this process based on frictions in the accumulation of customers, across and within markets segmented by geography. We use matched retail scanner and TV advertising data on consumer food to show that entrants grow both by adding customers in new markets and by reaching new customers in continuing markets. Growth in market share within markets is not associated with changes in markups, but is associated with advertising. We use these facts to motivate and estimate a structural model of customer accumulation within and across markets. This allows us to estimate both the distribution of intrinsic heterogeneity across firms, and frictions in the accumulation of customers. We find that these frictions contribute substantially to heterogeneity in firm size, and to the gradual process of firm growth.