The structure of the Nafion ionomer used in proton-exchange membranes of H(2)/O(2) fuel cells has long been contentious. Using a recently introduced algorithm, we have quantitatively simulated previously published small-angle scattering data of hydrated Nafion. The characteristic 'ionomer peak' arises from long parallel but otherwise randomly packed water channels surrounded by partially hydrophilic side branches, forming inverted-micelle cylinders. At 20 vol% water, the water channels have diameters of between 1.8 and 3.5 nm, with an average of 2.4 nm. Nafion crystallites (approximately 10 vol%), which form physical crosslinks that are crucial for the mechanical properties of Nafion films, are elongated and parallel to the water channels, with cross-sections of approximately (5 nm)(2). Simulations for various other models of Nafion, including Gierke's cluster and the polymer-bundle model, do not match the scattering data. The new model can explain important features of Nafion, including fast diffusion of water and protons through Nafion and its persistence at low temperatures.