The distal lung contains terminal bronchioles and alveoli that facilitate gas exchange. Three-dimensional in vitro human distal lung culture systems would strongly facilitate the investigation of pathologies such as interstitial lung disease, cancer and coronavirus disease 2019 (COVID-19) pneumonia caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Here we describe the development of a long-term feeder-free, chemically defined culture system for distal lung progenitors as organoids derived from single adult human alveolar epithelial type II (AT2) or KRT5 basal cells. AT2 organoids were able to differentiate into AT1 cells, and basal cell organoids developed lumens lined with differentiated club and ciliated cells. Single-cell analysis of KRT5 cells in basal organoids revealed a distinct population of ITGA6 ITGB4 mitotic cells, whose offspring further segregated into a TNFRSF12A subfraction that comprised about ten per cent of KRT5 basal cells. This subpopulation formed clusters within terminal bronchioles and exhibited enriched clonogenic organoid growth activity. We created distal lung organoids with apical-out polarity to present ACE2 on the exposed external surface, facilitating infection of AT2 and basal cultures with SARS-CoV-2 and identifying club cells as a target population. This long-term, feeder-free culture of human distal lung organoids, coupled with single-cell analysis, identifies functional heterogeneity among basal cells and establishes a facile in vitro organoid model of human distal lung infections, including COVID-19-associated pneumonia.