Habitat loss is the primary cause of local extinctions. Yet, there is considerable uncertainty regarding how fast species respond to habitat loss, and how time-delayed responses vary in space. We focused on the Argentine Dry Chaco (c. 32 million ha), a global deforestation hotspot, and tested for time-delayed response of bird and mammal communities to landscape transformation. We quantified the magnitude of extinction debt by modelling contemporary species richness as a function of either contemporary or past (2000 and 1985) landscape patterns. We then used these models to map communities’ extinction debt. We found strong evidence for an extinction debt: landscape structure from 2000 explained contemporary species richness of birds and mammals better than contemporary and 1985 landscapes. This suggests time-delayed responses between 10 and 25 years. Extinction debt was especially strong for forest specialists. Projecting our models across the Chaco highlighted areas where future local extinctions due to unpaid extinction debt are likely. Areas recently converted to agriculture had highest extinction debt, regardless of the post-conversion land use. Few local extinctions were predicted in areas with remaining larger forest patches. Synthesis and applications. The evidence for an unpaid extinction debt in the Argentine Dry Chaco provides a substantial window of opportunity for averting local biodiversity losses. However, this window may close rapidly if conservation activities such as habitat restoration are not implemented swiftly. Our extinction debt maps highlight areas where such conservation activities should be implemented.