I study the implications of climate change on housing markets, mortgage credit, and private adaptation. Households are exposed to physical climate risks that damage housing and degrade land, which is inelastically supplied. While the exposure to climate risk weakens housing demand, I show that the materialization of climate change raises house prices over time, as habitable land becomes increasingly scarcer. In frictionless markets, price signals support efficient adaptation. However, credit-constrained households have weaker incentives to adapt to climate change, indicating that pricing alone may be insufficient. Unequal adaptation reinforces wealth inequality and contributes to further habitat loss. As this tightening credit constraints for future generations, the private adaptation gap widens over time. I show that a shift from constrained homeownership to a rental model with unconstrained owners can lead to more efficient adaptation.