Business dynamism — the process of firm entry, growth and exit — lies at the heart of modern endogenous growth models. While productivity differences have traditionally been seen as the main driving forces of business dynamism, a growing body of evidence suggests that customer acquisition is at least as important. In light of this evidence, we propose a novel endogenous growth model in which innovating firms must first acquire customers to sell their products. Estimating our model with aggregate and firm-level data, we find that expansions of firms’ customer bases (market sizes) boost their incentives to innovate and shift resources towards high-growth businesses (“gazelles”). Combined, these effects explain over 40% of aggregate growth and substantially change predictions about the efficacy of growth policies. Finally, we document support for key model predictions using firm-level micro-data.