We present results from an experiment that randomized the expansion of electric grid infrastructure in rural Kenya. Electricity distribution is the canonical example of a natural monopoly. Randomized price offers show that demand for electricity connections falls sharply with price. Experimental variation in the number of connections combined with administrative cost data reveals considerable scale economies, as hypothesized. However, consumer surplus is far less than total costs at all price levels, suggesting that residential electrification may reduce social welfare. We discuss how leakage, reduced demand (due to red tape, low reliability, and credit constraints), and spillovers may impact this conclusion.