A theoretical model is developed for large scale-length, one-dimensional thermal instabilities along the field lines in tokamak divertors. Calculated growth rates predict a divertor thermal instability under the conditions (low-plasma temperature and density and high-neutral densities at the divertor plate) at which detachment followed by large-scale divertor temperature and density redistributions are observed in several DIII-D [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159] discharges.