This paper studies the effects of rising income inequality on residential patterns and house prices within a city. I develop a monocentric city model where household location, house prices, and housing supply respond to changes in income distribution. The household chooses housing quality and a residential location within the city. The key feature of the model is that the net cost of living further the city centre consists of a common component, and a component that is increasing with income. The model can generate imperfect sorting of income across locations: there is income mixing at non-central locations; households at the top and bottom of the income distribution compete for central locations. When income inequality increases, the changes in equilibrium resemble the gentrification phenomenon: low-quality houses near the city center are replaced by high-quality ones, and poor residents move to affordable non-central locations. A greenbelt places pressures on house prices and reduces welfare when inequality increases, and the welfare loss is most significant for low-income households.