Semi-insulating GaAs exhibits, at a field of about 1 kV/cm, a strong non-Ohmic conduction and negative differential resistance and is consequently suitable for the investigation of nonlinear systems and deterministic chaos. In this paper we explain both experimentally and theoretically, how the homogeneous electric-field distribution loses its stability in favor of a stable, propagating, high-electric-field domain. Furthermore, we provide detailed information about the microscopic structure of the steady-state domain and we explain that the onset of chaos is related to the interaction between subsequent domains.