We present results from an experiment that randomized the expansion of electric grid infrastructure in rural Kenya. Electricity distribution is a canonical example of a natural monopoly. Our experimental variation in the number of connections, combined with administrative cost data, reveals considerable scale economies, as hypothesized. Randomized price offers indicate that demand for connections falls sharply with price, and is far lower than anticipated by policymakers. Among newly connected households, average electricity consumption is very low, implying low consumer surplus. Moreover, we do not find meaningful medium-run impacts on economic and non-economic outcomes. We discuss implications for current efforts to increase rural electrification in Kenya, and highlight how credit constraints, bureaucratic red tape, low reliability, leakage, and other factors may affect interpretation of the results.