Differences between island- and mainland-dwelling forms provide several classic ecological puzzles. Why, for instance, are island-dwelling passerine birds consistently larger than their mainland counterparts? We examine the ‘Dominance hypothesis’, based on intraspecific competition, which states that large size in island passerines evolves through selection for success in agonistic encounters. We use the Heron Island population of Capricorn silvereyes (Zosterops lateralis chlorocephalus), a large-bodied island-dwelling race of white-eye (Zosteropidae), to test three assumptions of this hypothesis; that (i) large size is positively associated with high fitness, (ii) large size is associated with dominance, and (iii) the relationship between size and dominance is particularly pronounced under extreme intraspecific competition. Our results supported the first two of these assumptions, but provided mixed evidence on the third. On balance, we suggest that the Dominance Hypothesis is a plausible mechanism for the evolution of large size of island passerines, but urge further empirical tests on the role of intraspecific competition on oceanic islands versus that on mainlands.