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. 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. Among newly connected households, average electricity consumption is very low, implying low consumer surplus. We do not find meaningful medium-run impacts on economic and noneconomic outcomes. We discuss implications for current efforts to increase rural electrification in Kenya and highlight how various factors may affect interpretation.