This paper identifies a new factor, the age of the housing stock, that affects where high- and low-income neighborhoods are located in U.S. cities. High-income households, driven by a high demand for housing services, tend to locate in areas of the city where the housing stock is relatively young. Because cities develop and redevelop from the center outward over time, the location of these neighborhoods varies over the city's history. The model predicts a suburban location for the rich in an initial period, when young dwellings are found only in the suburbs, while predicting eventual gentrification once central redevelopment creates a young downtown housing stock. Controlling for other determinants of where the poor live (e.g., proximity to amenities and public transit), empirical work indicates that if the influence of spatial variation in dwelling ages were eliminated, central-city/suburban disparities in neighborhood economic status would be reduced by up to 10 percentage points. Model estimates further predict that between 2000 and 2020, central-city/suburban differences in economic status will narrow in cities of all sizes, and especially in the larger metropolitan areas as American cities become more gentrified.