Places are stratified along a hierarchy, with the affluent occupying the most resource-rich neighborhoods. Affluent neighborhood advantages include safety, high quality schools, and proximity to jobs. An additional benefit may be local economic stability over time. In a national context of rising interpersonal income inequality since 1970 and of the Great Recession, trends in neighborhood persistence and change expose this spatial advantage of the affluent. Using census data from 1970 to 2010, I find increasing rates of stability in the affluence and poverty of neighborhoods through 2000, with declines during the last decade. I also find that rates of chronic poverty and persistent affluence are high, ranging between 30 and 35 percent of neighborhoods across the 40-year period. This study highlights the structural persistence of affluence and poverty of neighborhoods as a vehicle for perpetuating social inequality and economic segregation.