The construction process of many residential buildings in African cities proceeds very slowly and may take over a decade. I document this phenomenon in a newly assembled dataset containing information on the construction duration of individual buildings in Nairobi. To explain the stylized facts and understand their consequences, I develop a heterogeneous agent model with financial frictions in which households engage in the construction of individual housing units. The model is calibrated to match key characteristics of the housing market in Nairobi. Counterfactual simulations show that improvements in credit provision can (a) substantially speed up the expansion of the aggregate housing stock which facilitates rural-urban migration, and (b) increase the city’s density by enabling the construction of taller buildings. The model also predicts that in the absence of reliable savings accounts, investments in incomplete structures emerge as an alternative savings vehicle.