This paper argues for the significance of argument structure and linear order in the binding conditions of Balinese (an Austronesian language with about 3,000,000 speakers, primarily on the islands of Bali and western Lombok, Indonesia). Our analysis employs the theory of prominence due to Bresnan (1995a,b). We show that linear order, thematic prominence, and the term/oblique distinction are crucial to Balinese binding, while other aspects of syntactic rank (e.g. SUBJ versus OBJ) play little or no role. We propose to define binding at a level of argument structure incorporating the term/oblique distinction (following Manning 1994).