We study the orbital structure of a self-consistent N-body equilibrium configuration of a barred galaxy constructed from cosmological initial conditions. The value of its spin parameter λ is near the observed value of our Galaxy λ= 0.22. We classify the orbits in regular and chaotic using a combination of two different methods and find 60 per cent of them to be chaotic. We examine the phase space using projections of the 4D surfaces of section for test particles as well as for real N-body particles. The real particles are not uniformly distributed in the whole phase space but they avoid orbits that do not support the bar. We use frequency analysis for the regular orbits as well as for the chaotic ones to classify certain types of orbits of our self-consistent system. We find the main resonant orbits and their statistical weight in supporting the shape of the bar, and we emphasize the role of weakly chaotic orbits in supporting the boxiness at the end of the bar.