Epithelial tissues are composed of polarized cells with distinct apical and basolateral membrane domains. In the Drosophila ovarian follicle cell epithelium, apical membranes are specified by Crumbs (Crb), Stardust (Sdt), and the aPKC-Par6-cdc42 complex. Basolateral membranes are specified by Lethal giant larvae (Lgl), Discs large (Dlg), and Scribble (Scrib). Apical and basolateral determinants are known to act in a mutually antagonistic fashion, but it remains unclear how this interaction generates polarity. We have built a computer model of apicobasal polarity that suggests that the combination of positive feedback among apical determinants plus mutual antagonism between apical and basal determinants is essential for polarization. In agreement with this model, in vivo experiments define a positive feedback loop in which Crb self-recruits via Crb-Crb extracellular domain interactions, recruitment of Sdt-aPKC-Par6-cdc42, aPKC phosphorylation of Crb, and recruitment of Expanded (Ex) and Kibra (Kib) to prevent endocytic removal of Crb from the plasma membrane. Lgl antagonizes the operation of this feedback loop, explaining why apical determinants do not normally spread into the basolateral domain. Once Crb is removed from the plasma membrane, it undergoes recycling via Rab11 endosomes. Our results provide a dynamic model for understanding how epithelial polarity is maintained in Drosophila follicle cells.