We propose a model of firm volatility based on customer-supplier connectedness. We assume that customers' growth rate shocks influence the growth rates of their suppliers, larger suppliers have more customers, and the strength of a customer-supplier link depends on the size of the customer firm. When the size distribution becomes more dispersed, economic activity is concentrated among a smaller number of firms, the typical supplier becomes less diversified and its volatility increases. The model is consistent with a set of new stylized facts. At the macro level, the firm volatility distribution is driven by firm size dispersion; the latter explains common movements in firm-level total and residual volatility. At the micro level, we show that the concentration of customer networks is an important determinant of firm-level volatility.