Existing research has found an inverse relationship between urban density and the degree of income inequality within metropolitan areas, suggesting that, as cities spread out, they become increasingly segregated by income. This paper examines this hypothesis using data covering more than 160000 block groups within 359 US metropolitan areas over the years 1980, 1990, and 2000. The findings indicate that income inequality - defined by the variance of the log household income distribution - does indeed rise significantly as urban density declines. This increase, however, is associated with rising inequality within block groups as cities spread out. The extent of income variation exhibited between different block groups, by contrast, shows virtually no association with population density. There is, accordingly, little evidence that sprawl is systematically associated with greater residential segregation of households by income.