A novel nonlinear model is presented for the occurrence of current fluctuations at low temperatures in extrinsic semiconductors. It is based on impact ionization of shallow impurities and structure-forming processes leading to a current filament. Numerical investigations reproduce the current-voltage characteristics and reveal regular, quasiperiodic, and frequency-locked spontaneous current oscillations and a Ruelle-Takens-Newhouse transition to chaos in agreement with experimental observations in n-type GaAs.